Question

nate wants to visit his friend mac before going to the park. nates house is located at (-2, 4), while the park is located at (10, 2). find the location of macs house if it is half of the distance from nates house to the park. the location of macs house is ( )

Explanation:

Step1: Recall the mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let Nate's house be $(x_1,y_1)=(-2,4)$ and the park be $(x_2,y_2)=(10,2)$.

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

$x=\frac{-2 + 10}{2}=\frac{8}{2}=4$.

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

$y=\frac{4+2}{2}=\frac{6}{2}=3$.

Answer:

$(4,3)$