Find the Area of the Triangle (2,3) , (4,5) , (-3,3)

$(2, 3)$ , $(4, 5)$ , $(- 3, 3)$

Use the formula to find the area of the triangle with $3$ points $(A_{x}, A_{y})$ , $(B_{x}, B_{y})$ , $(C_{x}, C_{y})$ .

$Area = \frac{| A_{x} (B_{y} - C_{y}) + B_{x} (C_{y} - A_{y}) + C_{x} (A_{y} - B_{y}) |}{2}$

Substitute the points into the formula.

Substitute the values of the first point into the formula.

$\frac{| 2 (B_{y} - C_{y}) + B_{x} (C_{y} - 3) + C_{x} (3 - B_{y}) |}{2}$

Substitute the values of the second point into the formula.

$\frac{| 2 (5 - C_{y}) + 4 (C_{y} - 3) + C_{x} (3 - 1 \cdot 5) |}{2}$

Substitute the values of the final point into the formula.

$\frac{| 2 (5 - 3) + 4 (3 - 3) - 3 (3 - 1 \cdot 5) |}{2}$

Simplify to find the area of the triangle.

Simplify the numerator.

Subtract $3$ from $5$ .

$\frac{| 2 \cdot 2 + 4 (3 - 3) - 3 (3 - 1 \cdot 5) |}{2}$

Multiply $2$ by $2$ .

$\frac{| 4 + 4 (3 - 3) - 3 (3 - 1 \cdot 5) |}{2}$

Subtract $3$ from $3$ .

$\frac{| 4 + 4 \cdot 0 - 3 (3 - 1 \cdot 5) |}{2}$

Multiply $4$ by $0$ .

$\frac{| 4 + 0 - 3 (3 - 1 \cdot 5) |}{2}$

Multiply $- 1$ by $5$ .

$\frac{| 4 + 0 - 3 (3 - 5) |}{2}$

Subtract $5$ from $3$ .

$\frac{| 4 + 0 - 3 \cdot - 2 |}{2}$

Multiply $- 3$ by $- 2$ .

$\frac{| 4 + 0 + 6 |}{2}$

Add $4$ and $0$ .

$\frac{| 4 + 6 |}{2}$

Add $4$ and $6$ .

$\frac{| 10 |}{2}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$\frac{10}{2}$

Divide $10$ by $2$ .

$5$