Question

The midpoint of QR is M(-1, -3). one endpoint is Q(4.5, -8). find the coordinates of endpoint R.

(-6.5, 2)
(1.75, -5.5)
(10, -13)
(-10.5, 6)

Answer 1

Answer: R(-6.5, 2)

Explanation:

Given: M(-1,-3) Q(4.5, -8) R(x,y)=?

The coordinates of the point in the middle of the segment are equal to the arithmetic mean of the coordinates of its ends

`\displaystyle\\Hence,\ x_M=(x_Q+x_R)/(2)\\\\-1=(4.5+x_R)/(2) \\`

Multiply both parts of the equation by 2:

`-2=4.5+x_R\\\\-2-4,5=4.5+x_R-4.5\\\\-6.5=x_R\\\\Thus,\ x_R=-6.5`

`\displaystyle\\y_M=(y_Q+y_R)/(2) \\\\-3=(-8+y_R)/(2)`

Multiply both parts of the equation by 2:

`-6=-8+y_R\\\\-6+8=-8+y_R+8\\\\2=y_R\\\\Thus,\ y_R=2`

`So,\ R(-6.5,2)`