Year 6 Maths reasoning (SATs) · Position and coordinates · Lesson 6.3

Year 6 Maths reasoning (SATs): Reflecting shapes in axes and lines

Part of the Year 6 Maths reasoning (SATs) position and coordinates chapter. Chapter overview · whole chapter on one page

6.3

Reflecting shapes in axes and lines

Year 6
Reflect shapes in the axes and in lines such as x = 3 (Year 6)

Story. Ruth folds a paper flag along a line so that one half lies exactly on the other. The fold is a mirror line, and each point on one side has a matching point the same distance away on the other side.

Rule

A reflection flips a shape over a mirror line. Each point is the same distance from the line as its image, on the other side.

In the x-axis, the sign of y changes: (x, y) becomes (x, -y). In the y-axis, the sign of x changes: (x, y) becomes (-x, y). In the line x = k, x becomes 2k - x.

Key ideas

Reflection in the x-axis: (x, y) -> (x, -y).
Reflection in the y-axis: (x, y) -> (-x, y).
Reflection in x = 3: x -> 6 - x.

A triangle to reflect in the x-axis.

Worked example 6.3.1

Shape B has vertices (1, 2), (3, 2), (2, 4). It is reflected in the x-axis. Write the new coordinates in the same order.

Method. Reflecting in the x-axis: change the sign of y.

Find the rule for the x-axis. Reflecting in the x-axis means you change the sign of y.
change the sign of y
Apply the rule to each vertex. Each point moves to the same distance on the other side.
(1, 2) -> (1, -2) ; (3, 2) -> (3, -2) ; (2, 4) -> (2, -4)
Write the new vertices. Keep the vertices in the same order.
(1, -2), (3, -2), (2, -4)
Write the answer.
(1, -2), (3, -2), (2, -4)

Check. Each point is the same distance from the mirror line. ✓

Watch out. Points on the mirror line do not move.

Worked example 6.3.2

Shape C has vertices (1, 1), (2, 3), (4, 1). It is reflected in the line x = 3. Write the new coordinates in the same order.

Method. Reflecting in x = 3: x becomes 2 x 3 - x, and y stays the same.

Find the rule for x = 3. Each x moves to 2 x 3 - x, so the same distance is kept on the other side.
x -> 2 x 3 - x
Apply the rule. Keep the y-coordinate the same.
(1, 1) -> (5, 1) ; (2, 3) -> (4, 3) ; (4, 1) -> (2, 1)
Write the new vertices. Keep the vertices in the same order.
(5, 1), (4, 3), (2, 1)
Write the answer.
(5, 1), (4, 3), (2, 1)

Check. Each point is the same distance from x = 3. ✓

Watch out. Check one point: its distance to the line before and after must be the same.

Worked example 6.3.3

The point (3, 4) is reflected in the y-axis. Write the new point.

Method. In the y-axis, the sign of x changes.

Change the sign of x. x = 3 becomes -3.
x = -3
Keep y. y stays the same, so y = 4.
(-3, 4)
Write the answer.
(-3, 4)

Check. (-3, 4) is the same distance from the y-axis. ✓

Watch out

Watch out. When reflecting in x = 3, do not just change the sign. The point (2, 5) goes to (4, 5), because it is 1 unit left of the line.

Exam tip

Practice guide. Count the squares from the mirror line to each point, then count the same number on the other side.