Question

Clara created a coordinate grid of her city. The bowling alley is located at (10, 12) and the skating rink is located at (-6, -4). Halfway between the bowling alley and the skating rink is the movie theater. Clara's house is halfway between the movie theater and the skating rink. What are the coordinates of Clara's house? A. (6, 8)B. (2, 4)C. (-2, 0)D. (-4, 0)

Answer 1

First we need to know the coordinates of the movie theater, we can do this applying the midpoint formula:

$\begin{gathered} P(BA,SR)=(\frac{10-6}{2},\frac{12-4}{2})\text{ = (}\frac{4}{2},\frac{8}{2}) \\ \Rightarrow P(BA,SR)=(2,4) \end{gathered}$

We have that the movie theater is located at (2,4). Now we use this coordinates to find the location of Clara's house using again the midpoint formula:

$\begin{gathered} P(MT,SR)=(\frac{-6+2}{2},\frac{4-4}{2})=(-\frac{4}{2},0) \\ \Rightarrow P(MT,SR)=(-2,0) \end{gathered}$

Therefore, Clara's house is located at (-2,0)