Coordinate Grid Worksheet for 11-Year-Olds: 2D Shapes, Lines, and Translation Exercises

Instructions

Welcome! This worksheet will test your knowledge of the coordinate grid. You will need a pencil and graph paper. Read each question carefully. For any questions that ask you to draw, please use a new coordinate grid for each problem to keep your work neat. Remember that coordinates are always written in the format (x, y). The x-coordinate tells you how far to move left or right, and the y-coordinate tells you how far to move up or down. Good luck!

Part A: Multiple Choice

Circle the best answer for each question.

1. What is the special name for the point (0, 0) on a coordinate grid?
   • a) The Center
   • b) The Origin
   • c) The Start
   • d) The Base
2. Which axis is the horizontal line that runs from left to right?
   • a) The origin-axis
   • b) The z-axis
   • c) The y-axis
   • d) The x-axis
3. In the coordinate pair (9, 2), what does the number 2 represent?
   • a) The y-coordinate
   • b) The x-coordinate
   • c) The quadrant number
   • d) The distance to the left
4. A point is located at (-4, 8). In which quadrant will you find it?
   • a) Quadrant I (+, +)
   • b) Quadrant II (-, +)
   • c) Quadrant III (-, -)
   • d) Quadrant IV (+, -)
5. A triangle has a corner at (5, 6). If the triangle is translated 4 units to the left and 1 unit down, what are the new coordinates of that corner?
   • a) (9, 7)
   • b) (1, 5)
   • c) (1, 7)
   • d) (9, 5)
6. Which of these points lies on the x-axis?
   • a) (0, 6)
   • b) (6, 6)
   • c) (-6, 6)
   • d) (6, 0)
7. If you connect the points (2, 2), (2, 5), and (6, 2) with lines, what shape do you form?
   • a) A square
   • b) An equilateral triangle
   • c) A right-angled triangle
   • d) A straight line
8. The instruction "translate 7 units down" means you should:
   • a) Add 7 to the x-coordinate
   • b) Subtract 7 from the x-coordinate
   • c) Add 7 to the y-coordinate
   • d) Subtract 7 from the y-coordinate
9. A rectangle has vertices at A(1,1), B(7,1), and C(7,4). What are the coordinates of the fourth vertex, D?
   • a) (1, 7)
   • b) (4, 7)
   • c) (1, 4)
   • d) (4, 1)
10. A point moves from (-2, -5) to (3, -5). What was the translation?
    • a) 5 units right
    • b) 5 units left
    • c) 1 unit up
    • d) 10 units down

Part B: True or False

Read each statement. Write 'True' or 'False' on the line next to it.

11. The y-coordinate is always written first in a coordinate pair. __________
12. Quadrant IV contains points where the x is positive and the y is negative (+, -). __________
13. Translating a shape changes its size and orientation. __________
14. The point (-8, -1) is in Quadrant III. __________
15. To move a point to the right, you add to its x-coordinate. __________
16. The points (5, 1) and (1, 5) are located at the same position. __________
17. A line connecting (-3, 4) and (5, 4) is a horizontal line. __________
18. Translating a shape 2 units up and then 2 units down will return it to its original position. __________
19. The point (0, -9) is on the y-axis. __________
20. Connecting points A(1,1), B(5,1), C(5,5), and D(1,5) in order will form a square. __________

Part C: Drawing and Short Answers

For this section, use graph paper to draw your coordinate grids and shapes.

21. Draw a coordinate grid that goes from -8 to 8 on both axes. Plot and label the following points:
    A(2, 6), B(-4, 3), C(-7, -1), D(5, -5)
22. Plot the points P(1, 1), Q(7, 1), and R(4, 6). Connect the points to form a triangle. What type of triangle is it? (Hint: Look at the side lengths).
23. A kite has vertices at E(-2, 3), F(1, 5), G(4, 3), and H(1, -4). Plot this shape on a coordinate grid.
24. Take the kite from question 23. Translate it 3 units left and 2 units up. What are the coordinates of the new vertices (E', F', G', H')?
25. Draw the new translated kite (E', F', G', H') on the same coordinate grid as the original.
26. Plot and connect these points in order: A(2, 2), B(8, 2), C(6, 6), D(0, 6). Connect D back to A. What is this shape called?
27. A rectangle has a corner at (-4, -3). Its length is 6 units and its width is 4 units. If the rectangle is drawn entirely to the right and up from this corner, what are the coordinates of the other three vertices?
28. A video game character starts at point M(7, -9). To get a treasure, it must be translated 10 units left and 12 units up. What are the coordinates of the treasure, M'?
29. A shape has vertices at L(-5, -2), M(-1, -2), N(-1, -7), and O(-5, -7). Plot the shape and identify it.
30. Describe the translation that moves point T(-4, 8) to point T'(2, 5).

Answer Key

Part A: Multiple Choice

1. b) The Origin
2. d) The x-axis
3. a) The y-coordinate
4. b) Quadrant II (-, +)
5. b) (1, 5)
6. d) (6, 0)
7. c) A right-angled triangle
8. d) Subtract 7 from the y-coordinate
9. c) (1, 4)
10. a) 5 units right

Part B: True or False

11. False
12. True
13. False (Translation only changes position, not size or orientation)
14. True
15. True
16. False
17. True
18. True
19. True
20. True (A square has four equal sides and four right angles)

Part C: Drawing and Short Answers

21. Student's grid should show the four points correctly plotted and labeled in their respective quadrants.
22. Isosceles Triangle (Sides PQ and QR are the same length).
23. Student's grid should show the four points connected to form a kite shape.
24. E'(-5, 5), F'(-2, 7), G'(1, 5), H'(-2, -2)
25. Student's grid should show the original kite and the new, translated kite in the correct positions.
26. Isosceles Trapezoid (or simply Trapezoid).
27. The other three vertices are (2, -3), (2, 1), and (-4, 1).
28. M'(-3, 3)
29. The shape is a rectangle.
30. Translate 6 units right and 3 units down.