Question

Mark is playing baseball after school. He wants to find the total distance he will need to ride his bike from school to the park, where his game will be played. Find the distance Mark will ride to the park from school. Leave your answer in simplest radical form if necessary.

√13
2√5
5
6

Answer 1

Use the distance formula (derived from Pythagorean Theorem:

`d = \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) } \\ = \sqrt{ {(10 - 8)}^(2) + {(11 - 7)}^(2) } \\ = \sqrt{ {(2)}^(2) + {(4)}^(2) } = √(4 + 16) \\ d = √(20)`

`d = √(20) = √(4) * √(5) = 2 √(5)`

Answer 2

B.
`2√(5)`

Explanation:

We have been given a map of different places on coordinate plane. We are asked to find the distance Mark will ride to the park from school.

To find the distance between school and park, we will use distance formula.

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

Let coordinates of school be
`(8,7)=(x_1,y_1)` and coordinates of park be
`(10,11)=(x_2,y_2)`.

Upon substituting coordinates of school and park in distance formula we will get,

`\text{Distance between park and school}=√((10-8)^2+(11-7)^2)`

`\text{Distance between park and school}=√((2)^2+(4)^2)`

`\text{Distance between park and school}=√(4+16)`

`\text{Distance between park and school}=√(20)`

`\text{Distance between park and school}=√(4\cdot 5)`

`\text{Distance between park and school}=2√(5)`

Therefore, Mark will ride
`2√(5)` units to the park from school and option B is the correct choice.