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SATs practice · Year 6Chapter 6 · Position and coordinates
Year 6 Maths reasoning (SATs) · Position and coordinates · Lesson 6.1

Year 6 Maths reasoning (SATs): Coordinates in four quadrants

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

6.1

Coordinates in four quadrants

Year 6
Describe positions on a full coordinate grid with all four quadrants (Year 6)
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. A treasure map has a grid with the origin in the middle. The pirate says the chest is at (-3, 2), which is left of the middle and above it. Mia must plot the point in the right quadrant.

Rule

The grid has an x-axis (across) and a y-axis (up and down). Points are written (x, y), x first.

The quadrants go anticlockwise from the top right: first (+, +), second (-, +), third (-, -), fourth (+, -).

Key ideas

  • x first, then y: (3, -2) is 3 right and 2 down.
  • First quadrant: both positive. Third quadrant: both negative.
  • A point on an axis is in no quadrant.
-5-5-4-4-3-3-2-2-1-11122334455
A triangle on a coordinate grid.
Worked example 6.1.1
Write the coordinates of the top vertex of the triangle in the picture.

Method. The top vertex is the highest point; read x first, then y.

  1. Read x. The vertex is 2 steps right of the y-axis.
    x = 2
  2. Read y. It is 5 steps up from the x-axis.
    y = 5
  3. Write the point. Write x first, then y.
    (2, 5)
  4. Write the answer.
    (2, 5)

Check. (2, 5): 2 right and 5 up. ✓

Worked example 6.1.2
The point (-3, 2) is in which quadrant? Write first, second, third or fourth.

Method. Look at the signs of the x- and y-coordinates.

  1. Look at the sign of x. x = -3, which is negative.
    x < 0
  2. Look at the sign of y. y = 2, which is positive.
    y > 0
  3. Name the quadrant. x is negative and y is positive, so the point is in the second quadrant.
    second
  4. Write the answer.
    second

Check. Quadrant 1 is ++, 2 is -+, 3 is --, 4 is +-. ✓

Watch out. Quadrants go anticlockwise from the top right: first, second, third, fourth.

Worked example 6.1.3
The point (-2, -4) is in which quadrant? Write first, second, third or fourth.

Method. Look at the signs of the x- and y-coordinates.

  1. Look at the sign of x. x = -2, which is negative.
    x < 0
  2. Look at the sign of y. y = -4, which is negative.
    y < 0
  3. Name the quadrant. x is negative and y is negative, so the point is in the third quadrant.
    third
  4. Write the answer.
    third

Check. Quadrant 1 is ++, 2 is -+, 3 is --, 4 is +-. ✓

Watch out. Quadrants go anticlockwise from the top right: first, second, third, fourth.

Watch out

Watch out. Always write x first. (3, -2) and (-2, 3) are different points.

Exam tip

Practice guide. Count from the origin: across first, then up or down.

Exercise 6A  Practice: four quadrants and reading points

Non-calculator
1
FThe point (4, 5) is in which quadrant? Write first, second, third or fourth.
2
FThe point (-6, 1) is in which quadrant? Write first, second, third or fourth.
3
FThe point (-2, -7) is in which quadrant? Write first, second, third or fourth.
4
FThe point (5, -3) is in which quadrant? Write first, second, third or fourth.
5
FWhat are the coordinates of the point 3 squares to the left of the origin and 4 squares down?
6
FWhich point is (-3, 4)? Choose one: (-3, 4), (4, -3) or (3, -4).
7
FTick the points that are in the second quadrant. Options: (-2, 3) | (2, 3) | (-2, -3) | (-5, 1). Write the options you would tick, in the order given.
8
PSHow many units apart are the points (-2, 3) and (-2, -4)? Write the number.
9
PSA treasure map starts at (-2, -1). The pirate moves up 5 squares. What are the new coordinates?
10
RExplain why the point (0, 5) is not in any quadrant.
11
RSam says that (-3, -3) and (3, 3) are reflections of each other in the x-axis. Is he right? Write yes or no.
12
FWrite the coordinates of the vertices of this triangle, starting at the bottom left and going anticlockwise.
-5-5-4-4-3-3-2-2-1-11122334455
13
FA point is 5 squares right of the y-axis and 2 squares below the x-axis. Write its coordinates.
14
RBen plots the points (4, 3), (-4, 3), (-4, -3) and (4, -3). What shape do they make, and is it a square or a rectangle? Write square or rectangle.

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