Basic Math Examples

(0, 0)

$(0, 0)$ ,

(1, 1)

$(1, 1)$ ,

(2, 0)

$(2, 0)$

Step 1

Use the formula to find the area of the triangle with

3

$3$ points

(A_{x}, A_{y})

$(A_{x}, A_{y})$ ,

(B_{x}, B_{y})

$(B_{x}, B_{y})$ ,

(C_{x}, C_{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}

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

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}

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

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}

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

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}

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

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

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

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

$1$ and

0

$0$ .

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

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

Step 3.1.2

Multiply

0

$0$ by

1

$1$ .

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

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

Step 3.1.3

Multiply

0 + 0

$0 + 0$ by

1

$1$ .

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

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

Step 3.1.4

Add

0

$0$ and

0

$0$ .

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

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

Step 3.1.5

Multiply

- 1

$- 1$ by

1

$1$ .

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

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

Step 3.1.6

Subtract

1

$1$ from

0

$0$ .

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

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

Step 3.1.7

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

Step 3.1.8

Add

0

$0$ and

0

$0$ .

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

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

Step 3.1.9

Subtract

2

$2$ from

0

$0$ .

\frac{| - 2 |}{2}

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

Step 3.1.10

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

- 2

$- 2$ and

0

$0$ is

2

$2$ .

\frac{2}{2}

$\frac{2}{2}$

\frac{2}{2}

$\frac{2}{2}$

Step 3.2

Divide

2

$2$ by

2

$2$ .

1

$1$

1

$1$

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