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 1/2 of the distance from Nates house to the park

Answer 1

(4, 3)

Explanation:

If a point O(x, y) divides a line segment AB with end points at A(
`x_1,y_1`) and B(
`x_2,y_2`) in the ratio of n:m, then the location of O is at:

`x=(n)/(n+m) (x_2-x_1)+x_1\\\\y=(n)/(n+m) (y_2-y_1)+y_1`

Given that Nates house is located at (-2,4) while the park is located at (10,2). Macs house if it is 1/2 of the distance from Nates house to the park (that is in the ratio of 1:1). Let (x, y) be the coordinate of Macs house, therefore:

`x=(1)/(2)(10-(-2))+(-2)=(1)/(2)(12)-2=6-2\\\\x= 4\\\\y=(1)/(2)(2-4) +4=(1)/(2)(-2)+4\\\\y=3`

The location of Macs house is (4, 3)