Question

Three houses A B and Clie on the same line on a map. House Blies exactly in the middle of house A and house C The point (3,6) on the

map represents house A and the point (-5-3) represents house B.

Find the coordinates of house Con the map

Answer 1

(-13, -12)

Explanation:

The midpoint (x,y) between two points (
`x_1,y_1`) and (
`x_2,y_2`) on the coordinate plane is given by:

`x=(x_1+x_2)/(2);\\\\y=(y_1+y_2)/(2)`

Hence given that house A is at (3, 6) and house B is at (-5, -3). Since house B is placed at the middle of house A and house B, let the coordinates of house C be (
`x_2,y_2`). Hence:

`-5=(3+x_2)/(2\\) \\3+x_2=-10\\\\x_2=-10-3\\\\x_2=-13`

`-3=(6+y_2)/(2\\) \\6+y_2=-6\\\\y_2=-6-6\\\\y_2=-12`

Therefore house C is at (-13, -12)