### Home > CCG > Chapter Ch7 > Lesson 7.1.3 > Problem7-29

7-29.

Remember that a midpoint of a line segment is the point that divides the segment into two segments of equal length. On graph paper, plot the points $P(0,3)$ and $Q(0,11)$. Where is the midpoint $M$ if $PM=MQ$? Explain how you found your answer.

Plot the points at their given coordinates.

Divide the length by two in order to find the length of $\overline{PM}$ and $\overline{MQ}$.

To find the coordinates of the midpoint, take the coordinates of either Point $P$ or Point $Q$ and add or subtract, respectively, the length of $\overline{PM}$ and $\overline{MQ}$ to the $y$-value.
Check your answer by placing the point at the coordinates you found.

Because the $x$-values of the two points are the same, the length of the segment is equal to the difference between the $y$-values of the two points.

Use the eTool below to model the problem.
Click the link at right for the full version of the eTool: CCG 7-29 HW eTool (Desmos)