Question

Triangle CDE, with vertices C(-8,-7), D(-2,-8) and E(-5,-2), is drawn on the coordinate grid below.

Answer 1

Answer:

Area = 24.75 sqr units

Step-by-step explanation:

You will need these formulas:

$d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}$

Midpoint = $(\frac{x_{1} + y_{1} }{2} , \frac{x_{2} + y_{2} }{2})$

Area = b x h

Let us treat CD as the base. Find the length of the base with the distance formula. Use the coordinates for points C & D.

$d = \sqrt{(-2 - (-8))^2 + (-8-(-7))^2}$

$d = \sqrt{37}$

The base is $\sqrt{37}$.

The height is the distance between point E and the midpoint of line CD.

Midpoint of CD = $(\frac{-8 + (-7) }{2} , \frac{-2 + (-8) }{2})$ = ($-\frac{15}{2}$, $-5$)

Use the distance formula to find the height.

$d = \sqrt{(-5 - (-\frac{15}{2} ))^2 + (-2-(-5))^2}$

$d = \frac{\sqrt{61} }{2}$

Find the area with the two distances that were found.

Area = $(\sqrt{37}) (\frac{\sqrt{61} }{2})$

Area = $\frac{\sqrt{2257} }{2}$

Area = 24.75 sqr units