Coordinate Grid Worksheet for 11-Year-Olds: Learn Forms, Lines & Shapes, and 2D Shape Translation

Instructions

Welcome to the Coordinate Grid Challenge! Read each question carefully. For Parts A and B, write your answer in the space provided. For Parts C and D, you will need a piece of graph paper and a pencil to plot points and draw shapes to find the answers. Good luck!

Part A: The Coordinate Grid Basics

Fill in the blanks to complete the sentences.

1. The horizontal line on a coordinate grid is called the x-axis.
2. The vertical line on a coordinate grid is called the y-axis.
3. The point where the two axes intersect (cross) is called the origin.
4. The coordinates for the origin are (____, ____).
5. A coordinate pair, like (3, 5), is always written in the order (____, ____).
6. In a coordinate pair, the first number tells you how far to move along the x-axis (left or right).
7. In a coordinate pair, the second number tells you how far to move along the y-axis (up or down).
8. A full coordinate grid that includes negative numbers is divided into four sections called quadrants.
9. In Quadrant I, both the x and y coordinates are (positive / negative).
10. Any point located on the y-axis will always have an x-coordinate of ____.

Part B: Position and Coordinates

Answer the following questions about coordinate points.

11. A point has coordinates (7, 2). How many units to the right of the origin is it?
12. A point has coordinates (4, 9). How many units up from the origin is it?
13. Are the points (8, 1) and (1, 8) in the same location? (Yes / No)
14. To plot the point (5, 3), you start at the origin, move 5 units right, and then 3 units ____.
15. Which of these points would NOT be in Quadrant I? A(4, 5), B(1, 9), C(-2, 3)
16. If you draw a line connecting point (2, 2) and point (2, 6), would the line be horizontal or vertical?
17. If you draw a line connecting point (1, 5) and point (4, 5), would the line be horizontal or vertical?
18. What are the coordinates for a point that is 3 units to the left of the origin and 6 units up?
19. What are the coordinates for a point on the x-axis that is 10 units to the right of the origin?
20. What are the coordinates for a point on the y-axis that is 5 units below the origin?

Part C: Forming Lines and Shapes

For this section, you will need a piece of graph paper to plot your points and draw the shapes.

1. Plot the following points and connect them in order with straight lines: A(1, 2), B(1, 6), and C(5, 2). Connect point C back to point A. What shape have you made? What specific type of shape is it?
2. Plot these four points and connect them in order: D(2, 1), E(8, 1), F(8, 5), and G(2, 5). Connect point G back to point D. What shape is it? Calculate its perimeter (the distance around the shape).
3. A square has one corner at (2, 2). One side of the square is 3 units long. If the entire square is in Quadrant I, what are the coordinates for the other three corners?
4. Plot the points H(3, 8), I(7, 8), and J(3, 1). Find the coordinates of a fourth point, K, that would complete the shape to make a rectangle.
5. On your graph paper, draw a rocket ship using at least 6 points, all in Quadrant I. List the coordinates for each point (vertex) you used. (Answers will vary).

Part D: Translating 2D Shapes

Translation means sliding a shape to a new location without rotating or flipping it. Use graph paper for these questions, too!

6. A triangle has vertices (corners) at P(2, 3), Q(4, 7), and R(5, 3). Translate the entire triangle 3 units to the right and 2 units up. What are the coordinates of the new triangle, P', Q', and R'?
7. A rectangle has corners at A(1, 1), B(6, 1), C(6, 4), and D(1, 4). It is translated so that the new corner A' is at (3, 5). Describe the translation in words (e.g., "moved ___ units right/left and ___ units up/down").
8. Using the same translation from question 7, what are the new coordinates for points B', C', and D'?
9. Point X is at (-1, 5). It is translated 6 units right and 3 units down. What are the coordinates of the new point, X'?
10. A shape has a point at (9, 8). After a translation, the same point is now at (4, 2). Describe the translation that moved the shape.

Answer Key

Part A: The Coordinate Grid Basics

1. x-axis
2. y-axis
3. origin
4. (0, 0)
5. (x, y)
6. right
7. up
8. quadrants
9. positive
10. 0

Part B: Position and Coordinates

11. 7 units
12. 9 units
13. No
14. up
15. C(-2, 3)
16. Vertical
17. Horizontal
18. (-3, 6)
19. (10, 0)
20. (0, -5)

Part C: Forming Lines and Shapes

1. The shape is a triangle. Specifically, it is a right-angled triangle.
2. The shape is a rectangle. The length is 6 units (from 8-2) and the width is 4 units (from 5-1). The perimeter is 6 + 4 + 6 + 4 = 20 units.
3. The other three corners are at (2, 5), (5, 5), and (5, 2).
4. The coordinates for point K are (7, 1).
5. Answers will vary. An acceptable answer lists at least 6 coordinate points in Quadrant I that form a recognizable rocket shape. For example: Body at (2,1), (4,1), (4,7), (2,7). Nose-cone at (3,9). Fins at (1,2) and (5,2).

Part D: Translating 2D Shapes

6. P' is at (5, 5). Q' is at (7, 9). R' is at (8, 5).
7. The translation was 2 units to the right and 4 units up. (To get from x=1 to x=3 is +2. To get from y=1 to y=5 is +4).
8. B' is at (8, 5). C' is at (8, 8). D' is at (3, 8).
9. X' is at (5, 2). (-1 + 6 = 5; 5 - 3 = 2).
10. The translation was 5 units to the left and 6 units down. (To get from x=9 to x=4 is -5. To get from y=8 to y=2 is -6).