## Intermediate Algebra (12th Edition)

$Q(3,-4)$
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, $P(7,10)$ and $Q(x,y)$. The midpoint is $M(5,3)$. Thus we have: $\displaystyle Midpoint=(\frac{7+x}{2},\ \frac{10+y}{2})=(5,3)$ We solve for $x$: $\frac{7+x}{2}=5$ $7+x=10$ $x=3$ And for $y$: $\frac{10+y}{2}=3$ $10+y=6$ $y=-4$ Therefore, the point Q is: $(3,-4)$