Question

Select the correct answer. a triangle on a coordinate plane with the nodes of (0, 0), (minus 2, 3) is represented as (x1, y1), and (5, 3) is represented as (x2, y1). what is the area of the triangle in the diagram? a. b. c. d.

Answer 1

The area of the triangle with vertices at (0,0), (-2,3), and (5,3) is calculated using the determinant method and is found to be 10.5 square units.

Step-by-step explanation:

The question asks for the area of a triangle on a coordinate plane with vertices at (0,0), (-2,3), and (5,3). To calculate the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3), you can use the following formula:

Area = \(|\frac{1}{2}| [(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))]

Plugging the coordinates of the vertices into the formula, we get:

Area = \(|\frac{1}{2}| [(0(3 - 3) + (-2)(3 - 0) + (5)(0 - 3))]

Area = \(|\frac{1}{2}| [0 - 6 - 15])

Area = \(|\frac{1}{2}| * -21)

Area = 10.5 square units (since area cannot be negative, we take the absolute value)

Therefore, the correct answer is that the area of the triangle is 10.5 square units.