Question

1) Sarah's house is at point (10, 14) and Melissa's house is at point (-8, 14). The two

friends want to meet at the park for a picnic, which is halfway between both houses.
How far will Sarah need to bike to reach the park? Round to the nearest tenth.

Answer 1

9.0

Explanation:

Use the midpoint formula:

`midpoint=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2))`

Insert the values of the points:

`(10,14)(-8,14)\\\\m=((10-8)/(2),(14+14)/(2))`

Simplify:

`m=((2)/(2),(28)/(2))\\\\m=(1,14)`

Now use the distance formula:

`d=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Plug in Sarah's home coordinates and the point of the park and solve:

`(10,14)(1,14)\\\\√((1-10)^2+(14-14)^2)`

Simplify parentheses:

`√((-9)^2+(0)^2)`

Simplify exponents:

`√(81) =9`

Round to the nearest tenth:

9.0

Finito.