Question

Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth.

Answer 1

The Area of the triangle with the coordinates given as A(-2, 2), B(6, 2), and C(0, 8) is 12 square units.

What is the Area of a Triangle with coordinates?

The study of geometry using coordinate points is known as coordinate geometry. If the triangle's three vertices are specified in the coordinate plane, the area of a triangle in coordinate geometry can be determined. In coordinate geometry, a triangle's area is the area or space it occupies in the 2-D coordinate plane.

In the given question, It is given the coordinate of vertices of the triangle.

A(-2, 2),

B(6, 2), and

C(0, 8)

and we know that the Area of the triangle with coordinates is given by:

$\text { Area }=1 / 2\left[\begin{array}{lll}x_1 & y_1 & 1 \\x_2 & y_2 & 1 \\x_3 & y_3 & 1\end{array}\right]$

That means:

$\text { Area }=(\frac{1}{ 2})\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$

Substituting the values to find the area:

$\text { Area }=(\frac{1}{ 2})| -2(2-2) + 6(8-2) +0(2-2)|$

Area = $\frac{24}{2}$

Area = 12 square units.

Hence, The Area of the triangle with the coordinates given as A(-2, 2), B(6, 2), and C(0, 8) is 12 square units.

To learn more about the area of the triangle, visit:

brainly.com/question/24372553

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