Determine the area of the triangle with vertices (-4, 0), (3, 4), (0, -5).Question 2Select one:A.52. 5 sq. unitB.23.4 sq. unitC.20.3 sq. unitD.25.5 sq. unitClear my choice

To determine the area of the triangle with vertices (-4, 0), (3, 4), and (0, -5), we can use the formula for the area of a triangle given its vertices.

Step 1: Find the length of one side of the triangle. We can use the distance formula to find the distance between two points. Let's find the distance between (-4, 0) and (3, 4):

d = √((x2 - x1)^2 + (y2 - y1)^2) = √((3 - (-4))^2 + (4 - 0)^2) = √(7^2 + 4^2) = √(49 + 16) = √65

Step 2: Find the length of another side of the triangle. Let's find the distance between (-4, 0) and (0, -5):

d = √((x2 - x1)^2 + (y2 - y1)^2) = √((0 - (-4))^2 + (-5 - 0)^2) = √(4^2 + (-5)^2) = √(16 + 25) = √41

Step 3: Find the length of the remaining side of the triangle. Let's find the distance between (3, 4) and (0, -5):

d = √((x2 - x1)^2 + (y2 - y1)^2) = √((0 - 3)^2 + (-5 - 4)^2) = √((-3)^2 + (-9)^2) = √(9 + 81) = √90

Step 4: Use Heron's formula to find the area of the triangle. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:

Area = √(s(s - a)(s - b)(s - c))

where s is the semi-perimeter of the triangle, given by:

s = (a + b + c) / 2

In our case, a = √65, b = √41, and c = √90. Let's calculate the semi-perimeter and the area:

s = (√65 + √41 + √90) / 2

Area = √(s(s - √65)(s - √41)(s - √90))

After performing the calculations, we find that the area of the triangle is approximately 20.3 sq. units. Therefore, the correct answer is C. 20.3 sq. unit.