Question

Find the coordinates of the other endpoint of the segment, given its midpoint M and one

Answer 1

Answer:

The coordinates of the other endpoint are (2b-g,2m-r)

Step-by-step explanation:

Let

R (x,y) ----> the other endpoint of the segment

we have

M(b,m) and Q(g,r)

we know that

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

In this problem the midpoint between Q and R is equal to the point M

substitute

$(b,m)=(\frac{g+x}{2},\frac{r+y}{2})$

$\frac{g+x}{2}=b$ ----> $x=2b-g$

$\frac{r+y}{2}=m$ ----> $y=2m-r$

therefore

The coordinates of the other endpoint are (2b-g,2m-r)