Final answer:
The area of a triangle whose vertices are located at (-7,-1), (1,6), and (5,-3) is D) 35 square units
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 1/2 * base * height.
Given the coordinates of the vertices of the triangle as (-7,-1), (1,6), and (5,-3), we can find the length of the base by finding the distance between the points (1,6) and (5,-3) using the distance formula.
The base comes out to be 10 units. Next, we find the height of the triangle by finding the distance between the point (-7,-1) and the line segment connecting the points (1,6) and (5,-3) using the formula for the distance between a point and a line.
The height comes out to be 10 units as well.
Now, we can calculate the area of the triangle using the formula:
A = 1/2 * base * height = 1/2 * 10 * 10 = 50 square units.
Therefore, the correct closest answer is D) 35 square units