Question

Given a triangle that has vertices at (-4,-3),(1,4), and (6,1) on the coordinate plane, determine the area of the triangle.

Answer 1

The area of the triangle with the given vertices is 24.5 square units.

Step-by-step explanation:

To find the area of a triangle given its vertices, we can use the formula: Area = 0.5 * [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)].

Using the given vertices (-4,-3), (1,4), and (6,1), we substitute the coordinates into the formula and calculate:

Area = 0.5 * [(-4)(4-1) + (1)(1-(-3)) + (6)(-3-4)] = 0.5 * [-12 + 12 - 49] = 0.5 * -49 = -24.5.

The area of the triangle is 24.5 square units.