Question

If $M$ is the mid-point of $AB$, find the co-ordinates of:
a) $A$ if the coordinates of $M$ and $B$ are $M(2,8)$ and $B(-4,19)$ and
b) $B$ if the coordinates of $A$ and $M$ are $A(-1,2)$, $M(-2,4)$.

Answer 1

(a) Let the point of $A$ be $(x,y)$

Then, $(\frac{x-4}{2},\frac{y+19}{2})=(2,8)$

$\frac{x-4}{2}=2,\frac{y+19}{2}=8$

$x=8,y=-3$

So, the point $A$ is $(8,-3)$

(b) Let the point $B$ be $(x,y)$

Then, $(\frac{x-1}{2},\frac{y+2}{2})=(-2,4)$

$\frac{x-1}{2}=-2,\frac{y+2}{2}=4$

$x=-3,y=6$

So, point $B$ is $(-3,6)$