Basic Math Examples

$(0, 0)$ , $(1, 1)$ , $(2, 0)$

Step 1

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

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

Step 2

Substitute the points into the formula.

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Step 2.1

Substitute the values of the first point into the formula.

$\frac{| 0 (B_{y} - C_{y}) + B_{x} (C_{y} + 0) + C_{x} (0 - B_{y}) |}{2}$

Step 2.2

Substitute the values of the second point into the formula.

$\frac{| 0 (1 - C_{y}) + 1 (C_{y} + 0) + C_{x} (0 - 1 \cdot 1) |}{2}$

Step 2.3

Substitute the values of the final point into the formula.

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

Step 3

Simplify to find the area of the triangle.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $1$ and $0$ .

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

Step 3.1.2

Multiply $0$ by $1$ .

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

Step 3.1.3

Multiply $0 + 0$ by $1$ .

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

Step 3.1.4

Add $0$ and $0$ .

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

Step 3.1.5

Multiply $- 1$ by $1$ .

$\frac{| 0 + 0 + 2 (0 - 1) |}{2}$

Step 3.1.6

Subtract $1$ from $0$ .

$\frac{| 0 + 0 + 2 \cdot - 1 |}{2}$

Step 3.1.7

Multiply $2$ by $- 1$ .

$\frac{| 0 + 0 - 2 |}{2}$

Step 3.1.8

Add $0$ and $0$ .

$\frac{| 0 - 2 |}{2}$

Step 3.1.9

Subtract $2$ from $0$ .

$\frac{| - 2 |}{2}$

Step 3.1.10

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{2}{2}$

Step 3.2

Divide $2$ by $2$ .

$1$

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