Distance & Translation Challenges in the Coordinate Plane

1. A point A is located at (2, 3) and point B is at (5, 7). What is the distance between points A and B?

• 7

• 3

• 4

• 5

2. If point C is at (4, 1) and you translate it 3 units to the right and 2 units up, what are the new coordinates of point C?

• (7, 3)

• (6, 1)

• (5, 3)

• (4, 4)

3. A park is represented on a coordinate plane. The entrance is at (0, 0) and the playground is at (6, 8). How far is the playground from the entrance?

• 8

• 12

• 5

• 10

4. Translate point D located at (1, 4) 5 units to the left. What are the new coordinates of point D?

• (1, 0)

• (6, 4)

• (-4, 4)

• (1, 9)

5. A delivery truck starts at point (3, 2) and needs to deliver a package to point (7, 6). Calculate the distance the truck travels between these two points.

• 8

• 3√2

• 4√2

• 6

• 5√2

6. If point E is at (2, 5) and you move it 4 units down and 1 unit left, what are the new coordinates of point E?

• (2, 4)

• (1, 6)

• (3, 5)

• (1, 1)

7. A school is located at (1, 1) and a library is at (4, 5). What is the distance between the school and the library?

• 5

• 6

• 7

• 3

8. Translate point F from (3, 3) to (3 units up and 2 units right. What are the new coordinates of point F?

• (1, 3)

• (3, 5)

• (5, 3)

• (5, 6)

9. A bike path runs from point (0, 0) to point (8, 6). How long is the bike path?

• 15

• 10

• 8

• 12

10. If point G is at (5, 5) and you translate it 2 units down and 3 units left, what are the new coordinates of point G?

• (3, 7)

• (5, 2)

• (8, 5)

• (2, 3)