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

On graph paper, draw Δ

*ABC*if*A*(2, 4),*B*(9, 5), and*C*(4, 10).*8-28 HW eTool*(Desmos). Homework Help ✎Verify that

*D*(3, 7) is a midpoint of*AC*.Write the equation of the line through points

*D*and*B*.Is

*BD*a height of Δ*ABC*? Use slope to show that*BD*is perpendicular to*AC*.What is the perimeter and area of Δ

*ABC*?

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

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*.

Compare the slopes of segment *BD* and segment *AC*. What do you notice?

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

Perimeter ≈ 20.467 units, Area = 20 units²

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