### Home > CCG > Chapter 8 > Lesson 8.3.1 > Problem8-98

8-98.

On graph paper, plot the points $A(−3, −1)$ and $B(6, 11)$.

1. Find the midpoint $M$ of $\overline {AB}$.

$\text{midpoint}=\left(\frac{x_1+x_2}{2}\frac{y_1+y_2}{2}\right)$

2. Find the point $P$, on $\overline {AB}$, that is $\frac { 2 } { 3 }$ of the way from $A$ to $B$.

Use the eTool below to visualize the problem.

3. Find the equation of the line that passes through points $A$ and $B$.

What is the $y$-intercept? What is the slope?

4. Find the distance between points $M$ and $P$.

Use a slope triangle drawn between $M$ and $P$, and the Pythagorean Theorem to calculate the distance.

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: 8-98 HW eTool (Desmos)