Question

madison wants to visit her friend olivia before going to the park. madison’s house is located at (-4, 6), while the park is located at (12, 8). find the location of olivia’s house if it is halfway between madison’s house and the park.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(-4,6)$ and $(x_2,y_2)=(12,8)$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{-4 + 12}{2}=\frac{8}{2}=4$.

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{6 + 8}{2}=\frac{14}{2}=7$.

Answer:

$(4,7)$