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

What is the area, in square units, of triangle CDE?

Triangle CDE, with vertices C(-8,-7), D(-2,-8) and E(-5,-2), is drawn on the coordinate-example-1

1 Answer

1 vote

Answer:

Area = 24.75 sqr units

Explanation:

You will need these formulas:


d = √((x_2 - x_1)^2 + (y_2-y_1)^2)

Midpoint =
((x_(1) + y_(1) )/(2) , (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 = √((-2 - (-8))^2 + (-8-(-7))^2)


d = √(37)

The base is
√(37).

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

Midpoint of CD =
((-8 + (-7) )/(2) , (-2 + (-8) )/(2)) = (
-(15)/(2),
-5)

Use the distance formula to find the height.


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


d = (√(61) )/(2)

Find the area with the two distances that were found.

Area =
(√(37)) ((√(61) )/(2))

Area =
(√(2257) )/(2)

Area = 24.75 sqr units

User Grant Zhu
by
7.6k points

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