QuestionFind the area of triangle $ABC$ with vertices $A(-7,4)$ , $B(-2,7)$ , and $C(-8,6)$ in square units.

Studdy Solution

STEP 1

Assumptions1. The vertices of the triangle ABC are A(-7,4), B(-,7), and C(-8,6). . The area of a triangle with vertices at (x1, y1), (x, y), and (x3, y3) is given by the formula $Area = \frac{1}{} |x1(y - y3) + x(y3 - y1) + x3(y1 - y)|$

STEP 2

First, we need to plug in the given values for the vertices into the formula for the area of a triangle.
$Area = \frac{1}{2} |-7(7 -6) -2(6 -4) -8(4 -7)|$

STEP 3

Now, we need to perform the operations inside the parentheses.
$Area = \frac{1}{2} |-7(1) -2(2) -8(-3)|$

STEP 4

Next, we need to perform the multiplication operations.
$Area = \frac{1}{2} |-7 -4 +24|$

STEP 5

Now, we need to perform the addition and subtraction operations.
$Area = \frac{1}{2} |13|$

STEP 6

The absolute value of13 is13.
$Area = \frac{1}{2} *13$

STEP 7

Finally, we need to perform the multiplication operation to find the area of the triangle.
$Area =6.5$ The area of triangle ABC is6.5 square units.

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