Question

Select the correct answer. What is the area of the triangle in the diagram? A. B. C. D. Reset Next Previous5 Next Using Coordinates to Compute Perimeters and Areas: Mastery Test Submit Test Tools Info © 2022 Edmentum. All rights reserved.

Answer 1

The area of the triangle can be calculated using the distance formula if the coordinates are given.

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle with coordinates on the coordinate plane.

It is required to find the area of the triangle using the coordinate points.

Here the coordinates are not given, so we are assuming the coordinates are (x1, y1), (x2, y2), (0,0)

From the distance formula:

The distance(b) between (0, 0) and (x1, y1):

$\rm b = \sqrt{(x_1-0)^2+(y_1-0)^2} \Rightarrow \sqrt{x_1^2+y_1^2}$

The distance between (0, 0) and (x2, y2):

$\rm h = \sqrt{(x_2-0)^2+(y_2-0)^2} \Rightarrow \sqrt{x_2^2+y_2^2}$

So the area of the triangle:

A = bh/2

$\rm A = \dfrac{1}{2}\times \sqrt{x_1^2+y_1^2} \times \sqrt{x_2^2+y_2^2}$

$\rm A = \dfrac{1}{2} \sqrt{(x_1^2+y_1^2) (x_2^2+y_2^2)}$

Thus, the area of the triangle can be calculated using the distance formula if the coordinates are given.

Learn more about the triangle here:

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