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

8-28.
  1. 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 AC.

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

    3. Is BD a height of ΔABC? Use slope to show that BD is perpendicular to AC.

    4. What is the perimeter and area of ΔABC?

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