If $( 2,3,1 )$ is the midpoint of the segment with one endpoint $( 1,3,1 )$ , find the second endpoint.
A) $( 3,3,1 )$
B) $\left( \frac { 3 } { 2 } , 3,1 \right)$
C) $( 1,0,0 )$
D) $( 0 , - 1,3 )$

Question

Quizplus · Accepted Answer

The midpoint formula in 3D is given by $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right)$. Given the midpoint $(2,3,1)$ and one endpoint $(1,3,1)$, we can find the other endpoint by solving for $x_2, y_2, z_2$. For $x$, $2 = \frac{1 + x_2}{2}$ gives $x_2 = 3$. $y$ and $z$ coordinates are the same as the midpoint, so the second endpoint is $(3,3,1)$.

If (2,3,1)( 2,3,1 )(2,3,1) Is the Midpoint of the Segment with One Endpoint

If $( 2,3,1 )$ Is the Midpoint of the Segment with One Endpoint