Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q$.
-$\mathrm{P}(4,8)$ and $M\biggl(\frac{1}{2}, \frac{5}{2}\biggl)$
A) $Q(-3,-3)$
B) $Q(1,5)$
C) $Q\biggl(-\frac{7}{2},-\frac{11}{2}\biggl)$
D) $Q(-7,-11)$

Question

Quizplus · Accepted Answer

The midpoint formula is $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Given $P(4,8)$ and $M\left(\frac{1}{2}, \frac{5}{2}\right)$, we can find $Q$ by solving for $x_2$ and $y_2$. Solving the equations $\frac{4 + x_2}{2} = \frac{1}{2}$ and $\frac{8 + y_2}{2} = \frac{5}{2}$ gives $x_2 = -3$ and $y_2 = -3$, so $Q(-3,-3)$.

Suppose That Segment PQP QPQ Has the Given Coordinates for One Endpoint

Suppose That Segment $P Q$ Has the Given Coordinates for One Endpoint