Answer:
The first aid station is at the middle of the park.
Step-by-step explanation:
Given
[tex](0,0) \to[/tex] Origin of Fun
[tex](-7, 6) \to[/tex] Quadratics in Motion
[tex](-2, 14) \to[/tex]Towers of Trigonometry
[tex](5,8) \to[/tex] The Food Equation
[tex](-1,7)\to[/tex] 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) [tex](0,0)[/tex] and [tex](-2, 14)[/tex]
(2) [tex](5,8)[/tex] and [tex](-7, 6)[/tex]
Calculate midpoint using:
[tex]M = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]
For (1):
[tex]M = \frac{1}{2}(0 -2, 0 + 14)[/tex]
[tex]M = \frac{1}{2}(-2,14)[/tex]
[tex]M = (-1,7)[/tex]
For (2):
[tex]M = \frac{1}{2}(5 -7, 8 + 6)[/tex]
[tex]M = \frac{1}{2}(-2,14)[/tex]
[tex]M = (-1,7)[/tex]
From the above computation, we have midpoint to be:
[tex]M = (-1,7)[/tex]
Given that:
[tex](-1,7)\to[/tex] First aid station
We can conclude that the first aid station is at the middle of the park.
