### Home > CC4 > Chapter 8 > Lesson 8.1.2 > Problem8-28

8-28.

On graph paper, draw $ΔABC$ if $A(2, 4)$, $B(9, 5)$, and $C(4, 10)$. 8-28 HW eTool (Desmos). Homework Help ✎

1. Verify that $D(3, 7)$ is a midpoint of $\overline{AC}$.

To find the midpoint between two points (average $x$-coordinates, average $y$-coordinates).

2. Write the equation of the line through points $D$ and $B$.

Read Math Notes box in Lesson 2.3.2 on linear equations from slopes and/or points.

Calculate the slope between points $D$ and $B$.

Using the slope, the $x$- and $y$-coordinates from point $D$ or $B$, and slope intercept form ($y = mx + b$). Solve for $b$.

3. Is BD a height of $ΔABC$? Use slope to show that $\overline{BD}$ is perpendicular to AC.

Compare the slopes of segment $\overline{BD}$ and segment $\overline{AC}$. What do you notice?

4. What is the perimeter and area of $ΔABC$?

Use the Pythagorean Theorem to find the length of all missing sides.

Perimeter $≈ 20.467$ units, Area $= 20\text{ units}^2$

Use the eTool below to solve the problem.
Click the link at right for the full version of the eTool: Int1 8-28 HW eTool