Question

Does the location of the first aid station actually fall in the middle of the park? Provide mathematical calculations to support your answer.

Answer 1

The first aid station is at the middle of the park.

Explanation:

Given

`(0,0) \to` Origin of Fun

`(-7, 6) \to` Quadratics in Motion

`(-2, 14) \to`Towers of Trigonometry

`(5,8) \to` The Food Equation

`(-1,7)\to` First aid station

Solving (a): Plot the above points

See attachment for plot

Solving (b): Determine if the first aid station is at the center of the park

From the plot, we have the opposite points to be:

(1)
`(0,0)` and
`(-2, 14)`

(2)
`(5,8)` and
`(-7, 6)`

Calculate midpoint using:

`M = (1)/(2)(x_1 + x_2, y_1 + y_2)`

For (1):

`M = (1)/(2)(0 -2, 0 + 14)`

`M = (1)/(2)(-2,14)`

`M = (-1,7)`

For (2):

`M = (1)/(2)(5 -7, 8 + 6)`

`M = (1)/(2)(-2,14)`

`M = (-1,7)`

From the above computation, we have midpoint to be:

`M = (-1,7)`

Given that:

`(-1,7)\to` First aid station

We can conclude that the first aid station is at the middle of the park.