Question

Points A, B, and C form a triangle. Points A and B are shown on the coordinate plane below. Point C is a reflection of

point B across the x-axis What is the area of the triangle?

6 square units

12 square units

18 square units

36 square units

Answer 1

The answer is given below

Explanation:

Given that:

Point A = (-4,3) and point B = (2,3)

Since Point C is a reflection of point B across the x-axis, point C has the same x coordinate as point B but the value of the y coordinate is the opposite sign. Therefore the coordinate of point C is (2,-3). The distance between AB is given as:

`AB=√((3-3)^2+(2-(-4))^2)=√(6^2)=6\ units\\BC=√((-3-3)^2+(2-2)^2)=√(6^2)=6\ units\\`

The height of the triangle is BC and the base is AB. The area of triangle ABC is given as:

Area = 1/2 × base × height = 1/2 × 6 × 6 = 18 unit²