### Home > GC > Chapter 8 > Lesson 8.1.3 > Problem8-30

8-30.

On graph paper, plot $A(2, 2)$ and $B(14, 10)$.

1. If $C$ is the midpoint of $\overline {AB}$, $D$ is the midpoint of $\overline {AC}$, and $E$ is the midpoint of $\overline {CD}$, find the coordinates of $E$.

When finding the midpoint remember to calculate the average of the $x$-coordinates and the average of the $y$-coordinates for the two points.

2. What fraction of the distance from $A$ to $B$ is $E$?

Draw a slope triangle for $AB$ and a slope triangle for $AE$, then compare their side lengths.

3. Use the ratio from part (b) to find the coordinates of point $E$.

Use the eTool to visualize the problem.
Click the link at right for the full version of the eTool: 8-30 HW eTool (Desmos)