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

Answer:

(4, 3)

Step-by-step 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:

$x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1$

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:

$x=\frac{1}{2}(10-(-2))+(-2)=\frac{1}{2}(12)-2=6-2\\\\x= 4\\\\y=\frac{1}{2}(2-4) +4=\frac{1}{2}(-2)+4\\\\y=3$

The location of Macs house is (4, 3)