Q. 114 - Precalculus Enhanced with Graphing Utilities

Question

Completing a Line Segment Plot the points A = (-1, 8) and M = (2, 3) in the $xy$-plane. If M is the midpoint of a line segment AB, find the coordinates of B.

Step-by-Step Solution

Answer

The coordinate of B is $\left(5,-2\right)$

Step 1. Given Information

We have $A=\left(-1,8\right)$ and $M=\left(2,3\right)$.

M is the midpoint of AB.

Step 2. Plotting the points

Step 2. Finding coordinates of B

By Mid-Point Formula

$$\begin{gathered} M\left(2,3\right)=\left(\frac{-1+x_2}{2},\frac{-8+y_2}{2}\right) \\ 2=\frac{-1+x_2}{2}\Rightarrow 4=-1+x_2 \\ {x}_2=5 \\ and \\ \frac{-8+y_2}{2}=3\Rightarrow y_2=-2 \end{gathered}$$

Thus, $B\left(5,-2\right).$