Question

#3 (64%)
aaron and beth live on highway 61 and the intersection for interstate 87 is halfway between their homes. if the coordinates of aarons home are (5, - 5) and beths are (-3,1) what point represents the intersection of highway 61 and interstate 87? the use of the grid is optional.
(a) (8, - 6)
(b) (4, - 3)
(c) (2, - 4)
(d) (1, - 2)

mr. longo is trying to find the most convenient place to park his car so that its equidistant from his gym and his house. his house is located at h(-4,7) and his gym is at g(6,1). determine the coordinate point c where mr. longo should park his car so its an even distance from the gym to his house. plot it on the graph and state it.

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for first problem

For Aaron's point $(5,-5)$ and Beth's point $(-3,1)$, $x=\frac{5+( - 3)}{2}=\frac{2}{2}=1$ and $y=\frac{-5 + 1}{2}=\frac{-4}{2}=-2$. The mid - point is $(1,-2)$.

Step3: Solve for second problem

For Mr. Longo's house at $H(-4,7)$ and gym at $G(6,1)$, $x=\frac{-4 + 6}{2}=\frac{2}{2}=1$ and $y=\frac{7+1}{2}=\frac{8}{2}=4$. The point $C$ is $(1,4)$.

Answer:

For the first problem: D. $(1,-2)$
For the second problem: $(1,4)$