Question

The midpoint of an is me -2,-6 if the coordinates of a are 1,-4 what are the coordinates of b

Answer 1

Given:

$\text{ The midpoint of }\bar{AB}\text{ is }M(-2,-6).\text{ Co-ordinates of A are }(1,-4).$

Required:

What are the coordinates of B?

Explanation:

We know the mid-point of of line between two points is:

$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Now, let point B(x1, y1)

$\begin{gathered} (-2,-6)=(\frac{1+x_1}{2},\frac{-4+y_1}{2}) \\ \text{ Equate Co-ordinates} \\ \frac{1+x_1}{2}=-2 \\ 1+x_1=-4 \\ x_1=-5 \\ and \\ \frac{-4+y_1}{2}=-6 \\ -4+y_1=-12 \\ y_1=-8 \end{gathered}$$\text{ Point B is }(-5,-8)$

Answer:

Hence, (-5,-8) is point B.