Question

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

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

Answer 1

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

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=((x1+x2)/(2),(y1+y2)/(2))`

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

substitute

`(b,m)=((g+x)/(2),(r+y)/(2))`

`(g+x)/(2)=b` ---->
`x=2b-g`

`(r+y)/(2)=m` ---->
`y=2m-r`

therefore

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