Question

Find the area of ABC with vertices A(3,-6), B(5,-6), and C(7,–9).

Answer 1

Area of a triangle ABC with the given vertices is 3 square units.

Given that, the vertices of a triangle ABC, A(3,-6), B(5,-6), and C(7,–9).

What is the area of triangle formula in coordinate geometry?

In Geometry, a triangle is a three-sided polygon that has three edges and three vertices. The area of the triangle is the space covered by the triangle in a two-dimensional plane.

Area of a triangle = $\frac{1}{2} ( |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|)$

Here, (x1, y1) = A(3,-6), (x2, y2) = B(5,-6), and (x3, y3) = C(7,–9)

Now, the area of a triangle = 1/2 (|3(-6+9)+5(-9+6)+7(-6+6)|)

= 1/2 (|3(3)+5(-3)+7(0)|)

= 1/2 (|(9-15)|)

= 1/2 × 6

= 3 square units

Therefore, area of a triangle ABC with the given vertices is 3 square units.

To learn more about the area of a area of triangle with vertices visit:

brainly.com/question/26633662.

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