Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (b, x), endpoint (m, q)
A) $( 2 b - m , 2 x - q )$
B) $\left( \frac { b + m } { 2 } , \frac { x + q } { 2 } \right)$
C) $( b - m , x - q )$
D) $( 2 m - b , 2 q - x )$

Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (b, x), endpoint (m, q) 
A) $( 2 b - m , 2 x - q )$
B) $\left( \frac { b + m } { 2 } , \frac { x + q } { 2 } \right)$
C) $( b - m , x - q )$
D) $( 2 m - b , 2 q - x )$

Quizplus · Accepted Answer

The midpoint formula is $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Given the midpoint (b, x) and one endpoint (m, q), to find the other endpoint, you solve for $x_2$ and $y_2$, resulting in $x_2 = 2b - m$ and $y_2 = 2x - q$, which matches choice A.

Find the Coordinates of the Other Endpoint of the Segment (2b−m,2x−q)( 2 b - m , 2 x - q )(2b−m,2x−q)

Find the Coordinates of the Other Endpoint of the Segment $( 2 b - m , 2 x - q )$