Final answer:
To calculate the area of a triangle with vertices (-6,2), (7,5), and (-4,-1), we use a formula based on the coordinates. The calculation shows that the area of the triangle is 22.5 square units.
Step-by-step explanation:
To find the area of a triangle with given vertices (-6,2), (7,5), and (-4,-1), we can use the following formula based on the coordinates of the vertices:
Area = \( \frac{1}{2} |x_{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})| \)
For our vertices, substituting the values into the formula, we get:
Area = \( \frac{1}{2} |(-6)(5 - -1) + (7)(-1 - 2) + (-4)(2 - 5)| \)
Area = \( \frac{1}{2} |(-6)(6) + (7)(-3) + (-4)(-3)| \)
Area = \( \frac{1}{2} |(-36) + (-21) + (12)| \)
Area = \( \frac{1}{2} |-45| \)
Area = \( \frac{1}{2} \times 45 \)
Area = 22.5 square units
So, the area of the triangle formed by the given vertices is 22.5 square units.