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KS3 Maths · Year 7Chapter 10 · Transformations, congruence and similarity
Year 7 · Chapter 10

Transformations, congruence and similarity

By the end of this chapter you will be able to

  • Describe a translation with a vector, a reflection with its line, and a rotation with its angle and centre (the origin)
  • Find the coordinates of a shape after a translation, reflection or rotation
  • Use the rules SSS, SAS, ASA and RHS to decide whether two triangles are congruent
  • Enlarge a shape from a centre by a positive whole number or a fraction, and find the missing sides of similar shapes
  • Write the coordinates of a transformed point using algebra

You should already know

  • Coordinates in all four quadrants (Chapter 7)
  • Angles in triangles, and the properties of shapes (Chapter 9)
  • Ratio and scale factors (Chapter 8)

Where this leads

  • Similar triangles and trigonometry in Years 8 and 9
  • Vectors and matrix transformations in Years 9 and beyond

National Curriculum for England, Key Stage 3 mathematics, Year 7. Content: G6 congruence criteria for triangles (SSS, SAS, ASA, RHS) and the labelling conventions used with them, G8 properties of, and the results of, translations, reflections and rotations, G9 identify and construct congruent triangles; enlargement with positive whole-number and fractional scale factors, with and without a coordinate grid, G16 mathematical relationships in coordinates: the coordinates of transformed points, written with algebra.

Exercise P  Do you remember?

Non-calculator
1
FHow many lines of symmetry does a square have?
2
FWhich is larger, 2/3 or 3/5?
3
FHow many degrees are there in a triangle?
4
FEnlarge the number 3 by a scale factor of 2. What is the new number?
5
FWhat is the x-coordinate of the point (2, 3)?
10.1

Translations

Year 7
G8, G16
Video lesson: TranslationsComing soon
A lift moves a box 3 squares to the right and 2 squares up. Every point of the box moves by the same amount, so the box keeps its size and shape. This is a translation.

A translation is described by a vector (a, b): move a units across (positive is right) and b units up (positive is up). To translate a point (x, y) by (a, b), the image is (x + a, y + b).

AB

Key ideas

  • A translation moves every point the same distance in the same direction.
  • The vector (a, b): a across (right is +) and b up (up is +).
  • Image of (x, y) under the translation (a, b): (x + a, y + b).
  • A translation keeps the size, shape and orientation; it only moves the shape.
Worked example 10.1.1
Translate the point (2, 3) by the vector (4, −1).

Method. Add the vector to the point.

  1. Across. Add 4 to the x-coordinate.
    2 + 4 = 6
  2. Up or down. Add −1 to the y-coordinate.
    3 + (−1) = 2
  3. Write the answer. Check it against the question.
    (6, 2)

Check. Move 4 right and 1 down: (6, 2). ✓

Watch out. A negative vector component moves the other way.

Worked example 10.1.2
Describe the translation that maps (2, 1) to (5, 4).

Method. Find the difference between the points.

  1. Across. The x-coordinate changes from 2 to 5, so move 3 right.
    5 − 2 = 3
  2. Up. The y-coordinate changes from 1 to 4, so move 3 up.
    4 − 1 = 3
  3. Write the answer. Check it against the question.
    the vector (3, 3)

Check. (2, 1) + (3, 3) = (5, 4). ✓

Watch out. Subtract the first point from the second.

Worked example 10.1.3
Triangle A has vertices (1, 1), (3, 1) and (1, 4). Translate it by (−2, 3). Give the image of (3, 1).

Method. Add the vector to (3, 1).

  1. Add the vector. Add (−2, 3) to (3, 1).
    (3 − 2, 1 + 3)
  2. Work out. The image point is found from the sums.
    (1, 4)
  3. Write the answer. Check it against the question.
    (1, 4)

Check. The other vertices are (−1, 4) and (−1, 7). ✓

Watch out. Translate every vertex by the same vector.

Watch out

Watch out: (−2, 3) means move 2 left and 3 up. It is not the same as (3, −2).

Exam tip

Grown-up tip. Ask the pupil to trace the shape on tracing paper and slide it, to see that the size and shape stay the same.

Exercise 10A  Translations

Non-calculator
1
FTranslate (1, 2) by the vector (3, 4).
2
FTranslate (5, −1) by (−2, 3).
3
FTranslate the origin (0, 0) by the vector (−4, −2).
4
FDescribe the translation that maps (2, 2) to (6, 1).
5
FTranslate the triangle with vertices A(1, 1), B(3, 1) and C(3, 4) by (2, −3). Give the image of C.
6
FA square has corners (0, 0), (2, 0), (2, 2) and (0, 2). It is translated by (1, 3). Give the image of the top right corner.
7
FFind the vector that moves (4, 7) to (1, 5).
8
PSA ship is at (2, 3). It sails 5 units right and 4 units down. Write its new position.
9
PSA point maps to (6, −2) after a translation by (4, −3). What was the original point?
10
RDoes a translation change the size or the shape of a shape? Explain.
11
RSam says that a translation by (2, 3) followed by a translation by (−2, −3) returns every point to its start. Is Sam right?
10.2

Reflections

Year 7
G8
Video lesson: ReflectionsComing soon
A mirror shows a reflection of a face. Each point is the same distance from the mirror as the real point, but on the other side. In coordinates, a reflection in the x-axis changes the sign of y, and a reflection in the y-axis changes the sign of x.

A reflection is in a line called the mirror line. The image is the same distance from the mirror line, on the other side, at a right angle to it. Common mirror lines are the x-axis (y = 0), the y-axis (x = 0), and the line y = x.

Key ideas

  • Reflection in the x-axis: (x, y) → (x, −y).
  • Reflection in the y-axis: (x, y) → (−x, y).
  • Reflection in y = x: (x, y) → (y, x).
  • Each point is the same distance from the mirror line as its image.
Worked example 10.2.1
Reflect the point (2, 3) in the x-axis.

Method. The x-axis is y = 0, so y changes sign.

  1. Keep x. The x-coordinate stays the same.
    x = 2
  2. Change the sign of y. The point moves to the other side of the x-axis.
    y = −3
  3. Write the answer. Check it against the question.
    (2, −3)

Check. (2, 3) is 3 above the x-axis; (2, −3) is 3 below. ✓

Watch out. Only the sign of y changes.

Worked example 10.2.2
Reflect the point (−4, 1) in the y-axis.

Method. The y-axis is x = 0, so x changes sign.

  1. Change the sign of x. The point moves to the other side of the y-axis.
    x = −(−4) = 4
  2. Keep y. The y-coordinate stays the same.
    y = 1
  3. Write the answer. Check it against the question.
    (4, 1)

Check. (4, 1) is 4 from the y-axis, as (−4, 1). ✓

Watch out. Only the sign of x changes.

Worked example 10.2.3
Reflect the point (2, 5) in the line y = x.

Method. Swap the coordinates.

  1. Choose the rule. Decide what the question asks for before calculating.
    (5, 2)
  2. Swap. Reflecting in y = x swaps x and y.
    (5, 2)
  3. Write the answer. Check it against the question.
    (5, 2)

Check. The line y = x is the mirror; (2, 5) and (5, 2) are the same distance from it. ✓

Watch out. Swap the two numbers.

Watch out

Watch out: reflecting (2, 3) in the y-axis gives (−2, 3), not (2, −3). The y-axis changes x, not y.

Exam tip

Grown-up tip. Ask the pupil to fold a piece of squared paper along the mirror line and mark the image point.

Exercise 10B  Reflections

Non-calculator
1
FReflect (3, 2) in the x-axis.
2
FReflect (3, 2) in the y-axis.
3
FReflect (−4, 1) in the y-axis.
4
FReflect (2, 5) in the line y = x.
5
FReflect (−1, −3) in the x-axis.
6
FReflect (0, 4) in the line x = 2.
7
FReflect (3, 1) in the line y = 2.
8
FWhich mirror line maps (1, 3) to (3, 1)?
9
FTriangle with vertices (1, 1), (3, 1) and (1, 4) is reflected in the y-axis. Give the image of (3, 1).
10
FReflect (2, −1): (a) in the x-axis (b) in the y-axis
(a)(a) in the x-axis
(b)(b) in the y-axis
11
PSA shape has a point (5, 3) on one side of the y-axis. Write the coordinates of its mirror image in the y-axis.
12
RExplain why reflecting a shape in the same mirror line twice gives the original shape.
10.3

Rotations about the origin

Year 7
G8
Video lesson: Rotations about the originComing soon
A windmill blade turns about its centre. Each point moves round a circle, and the shape turns through the same angle. A rotation needs three facts: the centre, the angle, and the direction.

For a rotation about the origin (0, 0): a 90° anticlockwise turn maps (x, y) to (−y, x). A 180° turn maps (x, y) to (−x, −y). A 90° clockwise turn maps (x, y) to (y, −x).

Key ideas

  • Rotation needs the centre, the angle and the direction (clockwise or anticlockwise).
  • 90° anticlockwise about the origin: (x, y) → (−y, x).
  • 180° about the origin: (x, y) → (−x, −y).
  • 90° clockwise about the origin: (x, y) → (y, −x).
Worked example 10.3.1
Rotate (2, 1) by 90° anticlockwise about the origin.

Method. Use (x, y) → (−y, x).

  1. Choose the rule. Decide what the question asks for before calculating.
    (−1, 2)
  2. Write the rule. For 90° anticlockwise, the image is (−y, x).
    (−1, 2)
  3. Write the answer. Check it against the question.
    (−1, 2)

Check. Turn back 90° clockwise: (−1, 2) → (2, 1). ✓

Watch out. Swap and change one sign for 90° anticlockwise.

Worked example 10.3.2
Rotate (1, 4) by 180° about the origin.

Method. Use (x, y) → (−x, −y).

  1. Choose the rule. Decide what the question asks for before calculating.
    (−1, −4)
  2. Change both signs. A half turn reverses both coordinates.
    (−1, −4)
  3. Write the answer. Check it against the question.
    (−1, −4)

Check. A second half turn returns (1, 4). ✓

Watch out. Both signs change.

Worked example 10.3.3
Rotate (2, 1) by 90° clockwise about the origin.

Method. Use (x, y) → (y, −x).

  1. Choose the rule. Decide what the question asks for before calculating.
    (1, −2)
  2. Write the rule. For 90° clockwise, the image is (y, −x).
    (1, −2)
  3. Write the answer. Check it against the question.
    (1, −2)

Check. 90° anticlockwise gives (−1, 2), the opposite of this. ✓

Watch out. Clockwise swaps and changes the sign of the new y.

Watch out

Watch out: a 90° clockwise rotation is not the same as 90° anticlockwise. Check the direction every time.

Exam tip

Grown-up tip. Ask the pupil to turn a sheet of squared paper a quarter turn and mark the new point, to see the direction.

Exercise 10C  Rotations about the origin

Non-calculator
1
FRotate (3, 0) by 90° anticlockwise about the origin.
2
FRotate (3, 0) by 90° clockwise about the origin.
3
FRotate (1, 4) by 180° about the origin.
4
FRotate (−2, 5) by 90° anticlockwise about the origin.
5
FRotate (−2, 5) by 90° clockwise about the origin.
6
FRotate the triangle with vertices (1, 0), (2, 0) and (2, 1) by 180° about the origin. Give the image of (2, 1).
7
FDescribe fully the rotation that maps (1, 0) to (0, 1).
8
FRotate (1, 4) by 270° anticlockwise about the origin.
9
FA shape has a point at (1, 2). After a rotation about the origin, the image is (−1, −2). Describe the rotation.
10
FRotate (0, 2) about the origin: (a) 90° anticlockwise (b) 180°
(a)(a) 90° anticlockwise
(b)(b) 180°
11
PSThe hour hand of a clock turns from 12 to 3. What rotation is this, about the centre?
12
RExplain why the rule (x, y) → (−y, x) gives a 90° anticlockwise rotation. Use the point (1, 0).
10.4

Congruent triangles

Year 7
G6, G9
Video lesson: Congruent trianglesComing soon
A builder cuts two roof trusses from the same plan. If the sides and angles match exactly, the two triangles are congruent: they are the same shape and the same size, and one can be moved on top of the other.

Two triangles are congruent if one of these rules holds:

Two angles alone do not prove congruence: the triangles may be different sizes.

Key ideas

  • SSS: three pairs of equal sides.
  • SAS: two pairs of equal sides with the equal angle between them.
  • ASA: two pairs of equal angles with the equal side between them.
  • RHS: right-angled triangles with equal hypotenuse and one other equal side.
Worked example 10.4.1
Triangles have sides 3 cm, 4 cm and 5 cm, and the other triangle has sides 5 cm, 3 cm and 4 cm. Are they congruent?

Method. Check whether all three sides match.

  1. Compare the sides. The sides 3, 4 and 5 are the same in each triangle, in a different order.
    3, 4, 5 = 3, 4, 5
  2. Name the rule. Three equal sides is the SSS rule.
    SSS
  3. Write the answer. Check it against the question.
    Yes, by SSS

Check. The triangles can be placed on each other. ✓

Watch out. The order of the sides does not matter for SSS.

Worked example 10.4.2
Triangle A has sides 4 cm and 5 cm with a 60° angle between them. Triangle B has the same 4 cm and 5 cm sides with the 60° between them. Congruent?

Method. Check two sides and the angle between them.

  1. Compare. Two sides and the included angle are equal.
    4, 60°, 5
  2. Name the rule. Two sides and the angle between them is the SAS rule.
    SAS
  3. Write the answer. Check it against the question.
    Yes, by SAS

Check. The angle is between the two equal sides. ✓

Watch out. The angle must be between the sides given.

Worked example 10.4.3
Two triangles have two angles of 40° and 70°, and the side between them is 6 cm in both. Congruent?

Method. The side is between the two angles.

  1. Compare. Two angles and the side between them are equal.
    40°, 6 cm, 70°
  2. Name the rule. This is the ASA rule.
    ASA
  3. Write the answer. Check it against the question.
    Yes, by ASA

Check. Both angles and the side between them match. ✓

Watch out. The side must be between the two angles.

Watch out

Watch out: two triangles with the same three angles may have different sizes. Equal angles show similarity, not congruence.

Exam tip

Grown-up tip. Ask the pupil to cut two triangles from paper with the same measurements, then check by placing one on the other.

Exercise 10D  Congruence

Non-calculator
1
FTwo triangles have sides 5 cm, 6 cm and 7 cm. The other triangle has sides 5 cm, 6 cm and 7 cm. Congruent? Name the rule.
2
FTwo triangles have two sides of 4 cm and 5 cm, and the angle between them is 60° in both. Congruent? Name the rule.
3
FTwo triangles have angles of 50° and 60°, and the side between them is 8 cm in both. Congruent? Name the rule.
4
FTwo right-angled triangles have hypotenuse 10 cm and a second side 6 cm. Congruent? Name the rule.
5
RTwo triangles have angles 50°, 60° and 70°, but different sizes. Are they congruent?
6
FWhich congruence rule would you use for two triangles with sides 3 cm, 4 cm and 6 cm, and sides 3 cm, 4 cm and 6 cm?
7
FName the congruence rule for triangles with two equal sides and the angle between them equal.
8
FName the congruence rule for two right-angled triangles with equal hypotenuse and one other equal side.
9
FIn triangles ABC and DEF: (a) AB = DE, BC = EF and AC = DF. Which rule? (b) AB = DE, angle B = angle E and BC = EF. Which rule?
(a)(a) three sides equal
(b)(b) two sides and the angle between
10
PSTriangles have sides 3, 4 and 6 in each. Are they congruent? Which rule?
11
RExplain why AAA (three equal angles) does not prove that two triangles are congruent.
10.5

Enlargement and similar shapes

Year 7
G9
Video lesson: Enlargement and similar shapesComing soon
A photo 10 cm wide is enlarged to 25 cm wide for a poster. The photo and the poster are similar: they have the same shape, but the poster is bigger. All lengths are multiplied by the same scale factor, here 2.5.

An enlargement with a scale factor k multiplies every length by k. A scale factor greater than 1 makes the shape bigger. A scale factor between 0 and 1 makes it smaller. Similar shapes have equal angles and sides in the same ratio.

Key ideas

  • Scale factor k: every length is multiplied by k.
  • k > 1: enlargement. 0 < k < 1: reduction. k = 2 doubles lengths, and areas are multiplied by k2.
  • Similar shapes: equal angles, and corresponding sides in the same ratio.
  • Find the scale factor by dividing a new length by the original length.
Worked example 10.5.1
A rectangle has sides 3 cm and 4 cm. It is enlarged with scale factor 2. What are the new sides?

Method. Multiply each side by 2.

  1. Choose the rule. Decide what the question asks for before calculating.
    3 × 2 = 6 and 4 × 2 = 8
  2. Multiply. Each length is doubled.
    3 × 2 = 6 and 4 × 2 = 8
  3. Write the answer. Check it against the question.
    6 cm and 8 cm

Check. 6 ÷ 2 = 3 and 8 ÷ 2 = 4. ✓

Watch out. Multiply every length.

Worked example 10.5.2
Triangles have sides 3, 4 and 5. A similar triangle has a side of 6 corresponding to 3. Find the other two sides.

Method. Find the scale factor, then multiply.

  1. Find the scale factor. The side 3 becomes 6, so the scale factor is 6 ÷ 3 = 2.
    k = 2
  2. Multiply the other sides. 4 × 2 = 8 and 5 × 2 = 10.
    8 and 10
  3. Write the answer. Check it against the question.
    8 and 10

Check. 3, 4, 5 scaled by 2 give 6, 8, 10. ✓

Watch out. Use the scale factor for all sides.

Worked example 10.5.3
A shape is enlarged with scale factor ½. A side of 8 cm becomes what?

Method. Multiply by the scale factor ½.

  1. Choose the rule. Decide what the question asks for before calculating.
    8 × ½ = 4
  2. Multiply. Half of 8.
    8 × ½ = 4
  3. Write the answer. Check it against the question.
    4 cm

Check. 4 × 2 = 8. ✓

Watch out. A fraction scale factor makes the shape smaller.

Watch out

Watch out: the scale factor for the area is k2, not k. Enlarging by 2 makes the area 4 times as big.

Exam tip

Grown-up tip. Ask the pupil to draw a small triangle on squared paper and enlarge it by 2, counting the squares of each side.

Exercise 10E  Enlargement and similarity

Non-calculator
1
FA length of 4 cm is enlarged by scale factor 3. What is the new length?
2
FA length of 6 cm is enlarged by scale factor 2.5. What is the new length?
3
FA length of 10 cm is reduced by scale factor ½. What is the new length?
4
FTriangle A has sides 3, 4 and 5. Triangle B is similar with the shortest side 6. Find the longest side of B.
5
FEnlarge the point (1, 2) by scale factor 3 about the origin. Give the image.
6
FEnlarge the point (2, 1) by scale factor 2 about the origin. Give the image.
7
FReduce the point (−4, 6) by scale factor ½ about the origin. Give the image.
8
FA rectangle is 2 cm by 3 cm. A similar rectangle is 6 cm by 9 cm. What is the scale factor?
9
FTwo similar triangles have sides 4 and 6 for corresponding sides. The corresponding side of the other is 10. Find the side of the bigger triangle that corresponds to 6.
10
PSA photo 10 cm by 15 cm is enlarged so that the 10 cm side becomes 25 cm. What is the new length of the 15 cm side?
11
RExplain why all circles are similar, but not all rectangles are similar.
10.6

Coordinates and transformations with algebra

Year 7
G16, G8
Video lesson: Coordinates and transformations with algebraComing soon
A computer game moves a character from (x, y) to (x + 3, y − 1) with each step. The new position is found with algebra, using the same rule for every point.

A rule written with letters shows what happens to any point. For a translation by (a, b): (x, y) → (x + a, y + b). For an enlargement from the origin with scale factor k: (x, y) → (kx, ky).

TE

Key ideas

  • Translation by (a, b): (x, y) → (x + a, y + b).
  • Reflection in the y-axis: (x, y) → (−x, y).
  • Enlargement from the origin, scale factor k: (x, y) → (kx, ky).
  • Rotation 90° anticlockwise about the origin: (x, y) → (−y, x).
Worked example 10.6.1
Describe the image of (x, y) under the translation by (2, −3), using algebra.

Method. Add the vector to each coordinate.

  1. Add to x. Add 2 to the x-coordinate.
    x + 2
  2. Add to y. Add −3 to the y-coordinate.
    y − 3
  3. Write the answer. Check it against the question.
    (x + 2, y − 3)

Check. With (1, 1): (3, −2). ✓

Watch out. Add each part separately.

Worked example 10.6.2
Triangle with vertices (1, 1), (2, 1) and (1, 3) is enlarged by scale factor 2 about the origin. Give the image of (2, 1).

Method. Multiply each coordinate by 2.

  1. Choose the rule. Decide what the question asks for before calculating.
    (4, 2)
  2. Multiply. 2 × 2 and 1 × 2.
    (4, 2)
  3. Write the answer. Check it against the question.
    (4, 2)

Check. The other image points are (2, 2) and (2, 6). ✓

Watch out. Multiply both coordinates by k.

Worked example 10.6.3
Point (4, 2) is reflected in the line y = x. Write the image.

Method. Swap the coordinates.

  1. Choose the rule. Decide what the question asks for before calculating.
    (2, 4)
  2. Swap. Reflection in y = x swaps x and y.
    (2, 4)
  3. Write the answer. Check it against the question.
    (2, 4)

Check. Swapping again gives (4, 2). ✓

Watch out. Swap them.

Watch out

Watch out: the enlargement rule (kx, ky) is from the origin. For another centre, the distances from the centre must be scaled.

Exam tip

Grown-up tip. Ask the pupil to test a rule with a simple point, such as (1, 0) or (0, 1), before using it on the whole shape.

Exercise 10F  Coordinates and transformations

Non-calculator
1
FEnlarge (1, 3) by scale factor 2 from the origin. Give the image.
2
FEnlarge (−2, 5) by scale factor 3 from the origin. Give the image.
3
FTriangle (1, 1), (2, 1), (1, 3) is enlarged by scale factor 2 from the origin. Give the image of (1, 3).
4
FWrite the rule for a reflection in the y-axis, using algebra.
5
FWrite the rule for a translation by (2, −3), using algebra.
6
FPoint (4, 2) is reflected in the line y = x. Give the image.
7
FTranslate the point (2, −1) by the rule (x + 3, y + 1). Give the image.
8
FThe point (1, 2) is enlarged to (3, 6) from the origin. Find the scale factor.
9
FFor the point (3, 4): (a) reflect in the x-axis (b) rotate 90° anticlockwise about the origin
(a)(a) reflect in the x-axis
(b)(b) rotate 90° anticlockwise
10
PSA triangle has vertices (0, 0), (4, 0) and (0, 3). It is enlarged by scale factor ½ from the origin. Find the area of the image.
11
RExplain why enlarging a shape by scale factor 2 makes its area four times bigger.

Chapter summary

SkillMethod
Translation(x, y) → (x + a, y + b) for the vector (a, b)
ReflectionIn the x-axis: (x, −y); in the y-axis: (−x, y); in y = x: (y, x)
Rotation about the origin90° anticlockwise (−y, x); 180° (−x, −y); 90° clockwise (y, −x)
CongruenceSSS, SAS, ASA, RHS: the same shape and size; equal angles alone are not enough
EnlargementMultiply every length by the scale factor k; area by k²
SimilarityEqual angles and corresponding sides in the same ratio

Can you…?

  • I can translate a shape by a vector, and describe a translation
  • I can reflect a shape in the x-axis, the y-axis and the line y = x
  • I can rotate a shape by 90° or 180° about the origin, in the correct direction
  • I can use SSS, SAS, ASA and RHS to decide if two triangles are congruent
  • I can enlarge a shape by a whole-number or fractional scale factor, and find similar sides
  • I can write a transformation using algebra

Key terms

translation
a movement of every point of a shape by the same vector
vector
a movement described by how far it goes across and up or down
reflection
a flip of a shape in a mirror line
rotation
a turn of a shape about a centre by an angle, in a direction
congruent
the same shape and the same size
similar
the same shape, with equal angles and sides in the same ratio
scale factor
the number every length is multiplied by in an enlargement
enlargement
a transformation that changes the size of a shape from a centre by a scale factor

Exercise 10Z  Check-up

Non-calculator
1
Reflect (5, −2) in the x-axis.
2
Rotate (2, 3) by 90° clockwise about the origin.
3
Translate (−1, 4) by (3, −6).
4
Enlarge (3, −1) by scale factor 3 from the origin.
5
Two triangles have two sides and the angle between them equal. Which congruence rule?
6
Triangles have sides 2, 3 and 4 cm, and the similar triangle has a side of 4 cm for the side 2 cm. Find the scale factor.
7
Reflect (1, 5) in the line y = x.
8
Enlarge a square of side 3 cm by scale factor 2. What is the new area?
9
Rotate (1, 4) by 180° about the origin.
10
Write the image of (x, y) under the translation by (4, 1), using algebra.

Total 21 marks. Allow about 21 minutes.

Exercise 10X  Practice test questions

Non-calculator
1
FTranslate (1, 1) by the vector (4, −2).[1 mark]
2
FReflect (3, −5) in the x-axis. Give the image.[1 mark]
3
FRotate (2, −1) by 90° anticlockwise about the origin. Give the image.[2 marks]
4
FEnlarge the triangle with vertices (1, 1), (3, 1) and (3, 2) by scale factor 2 from the origin. Give the image of (3, 2).[2 marks]
5
FTriangle A has vertices (1, 1), (2, 1) and (1, 3). Triangle B has vertices (−1, 1), (−2, 1) and (−1, 3). Describe fully the single transformation.[2 marks]
6
FTriangles have sides 3, 4, 5 and sides 6, 8, 10. Are they similar? Find the scale factor.[2 marks]
7
FTriangles ABC and DEF have AB = DE, BC = EF and AC = DF. Which congruence rule applies?[2 marks]
8
FA rectangle 4 cm by 6 cm is enlarged by scale factor 2.5. Find the area of the new rectangle.[3 marks]
9
FA rotation of 90° clockwise about the origin maps P to (3, 2). Find the coordinates of P.[3 marks]
10
RExplain why two triangles with angles 40°, 60° and 80° in two different sizes are similar but not congruent.[3 marks]
← Chapter 9: Angles, polygons and constructionsChapter 11: Perimeter, area, volume and Pythagoras →

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