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Ignition Learning — Activity Sheet

The Cartesian plane & plotting points

Mathematics · Year 7

Name: ______________________Date: ____________

The Cartesian plane is a grid used to show the position of points using two numbers, called coordinates, written as (x, y). The x-coordinate tells you how far to move left or right (horizontal), and the y-coordinate tells you how far to move up or down (vertical), always starting from the origin (0, 0). The plane is divided into four quadrants by two perpendicular axes: the horizontal x-axis and the vertical y-axis.

Example

The point (3, 2) is found by starting at the origin, moving 3 units right along the x-axis, then 2 units up. The point (−2, 4) moves 2 units left and 4 units up.

Key terms

Coordinates:: A pair of numbers (x, y) that shows a point's position on the Cartesian plane.
Origin:: The point (0, 0), where the x-axis and y-axis cross.
Axis:: A reference line on the Cartesian plane — the x-axis is horizontal, the y-axis is vertical.

Questions

1. The Cartesian plane uses coordinates to show:
- Colours
- Position
- Time
- Weight
2. Coordinates are written as:
- (x, y)
- (y, x, z)
- x only
- A single number
3. The x-coordinate tells you:
- Up or down movement
- Left or right movement
- The colour
- The size
4. The y-coordinate tells you:
- Left or right movement
- Up or down movement
- The colour
- The size
5. The origin is the point:
- (1, 1)
- (0, 0)
- (10, 10)
- (-1, -1)
6. The x-axis is:
- Vertical
- Horizontal
- Diagonal
- Curved
7. The y-axis is:
- Vertical
- Horizontal
- Diagonal
- Curved
8. To plot (3, 2), you move:
- 3 up, 2 right
- 3 right, 2 up
- 2 right, 3 up
- 2 up, 3 left
9. To plot (-2, 4), you move:
- 2 right, 4 up
- 2 left, 4 up
- 2 left, 4 down
- 2 right, 4 down
10. What are the coordinates of the origin?
- (1,0)
- (0,1)
- (0,0)
- (1,1)
11. A point with a negative x-coordinate is located:
- To the right of the origin
- To the left of the origin
- Above the origin
- Below the origin
12. A point with a negative y-coordinate is located:
- Above the origin
- Below the origin
- To the left
- To the right
13. The point (0, 5) lies:
- On the x-axis
- On the y-axis
- In quadrant 1
- Nowhere
14. The point (5, 0) lies:
- On the x-axis
- On the y-axis
- In quadrant 1
- Nowhere
15. Which point is located 4 units left and 3 units down from the origin?
- (4,3)
- (-4,-3)
- (-4,3)
- (4,-3)
16. The Cartesian plane is divided into how many quadrants?
- 2
- 3
- 4
- 6
17. A point in quadrant 3 (bottom-left) has:
- Positive x, positive y
- Negative x, negative y
- Positive x, negative y
- Negative x, positive y
18. Which two points are the same distance from the origin along the x-axis, in opposite directions?
- (3,0) and (-3,0)
- (3,0) and (0,3)
- (2,2) and (3,3)
- (1,1) and (-1,-1)
19. If you move from point (2,2) to point (5,2), how far did you move?
- 3 units right
- 3 units up
- 3 units left
- 3 units down
20. The point (-3, -3) lies in which quadrant?
- 1
- 2
- 3
- 4

Answer key (parent copy)

1. Position
2. (x, y)
3. Left or right movement
4. Up or down movement
5. (0, 0)
6. Horizontal
7. Vertical
8. 3 right, 2 up
9. 2 left, 4 up
10. (0,0)
11. To the left of the origin
12. Below the origin
13. On the y-axis
14. On the x-axis
15. (-4,-3)
16. 4
17. Negative x, negative y
18. (3,0) and (-3,0)
19. 3 units right
20. 3