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

Question

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

Quizplus · Accepted Answer

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

Find the Coordinates of the Other Endpoint of the Segment (a−m,w−q)( \mathrm { a } - \mathrm { m } , \mathrm { w } - \mathrm { q } )(a−m,w−q)

Find the Coordinates of the Other Endpoint of the Segment $( \mathrm { a } - \mathrm { m } , \mathrm { w } - \mathrm { q } )$