Question

parks nate wants to visit his friend mac before going to the park. nates house is located at (-4, 4), while the park is located at (8, 6). find the location of macs house if it is $\frac{1}{2}$ of the distance from nates house to the park.

Explanation:

Step1: Use the mid - point formula

The mid - point formula between 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, $(x_1,y_1)=(-4,4)$ and $(x_2,y_2)=(8,6)$.

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

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

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

$y=\frac{4+6}{2}=\frac{10}{2}=5$.

Answer:

$(2,5)$