Exploring Distance and Midpoint with Coordinates in 8th Grade

1. A park is located at point A(2, 3) and a playground is at point B(8, 7). What is the distance between the park and the playground?

• 5 * sqrt(2)

• 3 * sqrt(10)

• sqrt(50)

• 2 * sqrt(13)

2. If a school is located at point C(4, 1) and a library is at point D(10, 5), what is the midpoint between the school and the library?

• (8, 4)

• (7, 3)

• (5, 3)

• (6, 2)

3. A bike path runs from point E(1, 2) to point F(5, 6). Calculate the distance of the bike path.

• 6

• 3√2

• 5

• 4√2

4. Two friends are standing at points G(3, 4) and H(7, 8). What is the distance between them?

• 3√2

• 4√3

• 5

• 2√5

5. A delivery truck starts at point I(0, 0) and needs to reach a warehouse at point J(6, 8). What is the distance the truck must travel?

• 8

• 10

• 12

• 15

6. The coordinates of a coffee shop are K(2, 5) and a bookstore are L(10, 1). Find the midpoint between the coffee shop and the bookstore.

• (6, 3)

• (8, 4)

• (5, 2)

• (4, 3)

7. A runner starts at point M(1, 1) and runs to point N(4, 5). How far does the runner travel?

• 3

• 4

• 5

• 7

8. A city is planning to build a new community center at point O(3, 3) and a new park at point P(9, 7). What is the distance between the two locations?

• √50

• 5√2

• 3√13

• 2√13

9. If a car is parked at point Q(2, 2) and needs to reach a gas station at point R(8, 10), what is the distance the car must drive?

• 5

• 15

• 12

• 10

10. A line segment connects points S(1, 1) and T(7, 3). What is the midpoint of this line segment?

• (4, 2)

• (6, 3)

• (3, 1)

• (5, 2)