## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 2 - Section 2.1 - Linear Equations in Two Variables - 2.1 Exercises: 77

#### Answer

$Q(11,-4)$

#### Work Step by Step

To find the midpoint between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the midpoint formula: $\displaystyle Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ We have the two points, $P(5,8)$ and $Q(x,y)$. The midpoint is $M(8,2)$. Thus we have: $\displaystyle Midpoint=(\frac{5+x}{2},\ \frac{8+y}{2})=(8,2)$ We solve for $x$: $\frac{5+x}{2}=8$ $5+x=16$ $x=11$ And for $y$: $\frac{8+y}{2}=2$ $8+y=4$ $y=-4$ Therefore, the point Q is: $(11,-4)$

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