Question

The midpoint of segment QR is M(-2, 9). One end point of segment QR is Q(-8, 12). Find the coordinates of the other endpoint, R.

Answer 1

Here,

The midpoint of segment QR is M

m(-2,9) x3=-2,y3=9

Q=(-8,12)x1=-8,y1=12

R=x2,y2

we know that,

$\tt{ m=\dfrac{Q+R}{2} }$ ⠀

So,

x3=$\tt{\dfrac{x1+x2}{2} }$ ⠀

$\tt{-2=\dfrac{-8+x2}{2} }$ ⠀

$\tt{-2×2=-8+x2 }$ ⠀

$\tt{x2=8-4 }$ ⠀

$\tt{x2=4 }$ ⠀

x2=4

now we find the y coordinate y2.

y3=$\tt{\dfrac{y1+y2}{2} }$ ⠀

$\tt{9=\dfrac{12+y2}{2} }$ ⠀

$\tt{9×2=12+y2 }$ ⠀

$\tt{y2=18-12 }$ ⠀

$\tt{y2=6 }$ ⠀

y2=6

Now we get the two coordinate of R

so,

R=(x2,y2)=(4,6)