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

Answer:

(-13, -12)

Step-by-step explanation:

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

$x=\frac{x_1+x_2}{2};\\\\y=\frac{y_1+y_2}{2}$

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:

$-5=\frac{3+x_2}{2\\} \\3+x_2=-10\\\\x_2=-10-3\\\\x_2=-13$

$-3=\frac{6+y_2}{2\\} \\6+y_2=-6\\\\y_2=-6-6\\\\y_2=-12$

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