Question

Use the distance formula and/or the Pythagorean Theorem to find the area of the triangle.

Answer 1

Answer:

B. 20.5 square units

Step-by-step explanation:

Area of a triangle = 1/2 * Base * Height

For the given triangle, the value for the sides will be the distance between adjacent points on the triangle. Look at the attached file for the explanation of the diagram.

Using the formula for finding the distance between two points to get the base and the height of the triangle.

D = √(x2-x1)²+(y2-y1)²

For side AB where A = (-3, -4) and B(2, 0)

AB = √(2-(-3))²+(0-(-4))²

AB = √5²+4²

AB = √25+16

AB = √41

AB = Height

For side BC where B = (2, 0) and C = (6, -5)

√(x2-x1)²+(y2-y1)²

BC = √6-2)²+(-5-0)²

BC= √4²+(-5)²

BC = √16+25

BC= √41

BC = base of the triangle

Area of the triangle = 1/2 * √41 * √41

Area of the triangle = 1/2 * 41

Area of the triangle =20.5square units