Pre-Algebra Examples

(1, 1)

$(1, 1)$ ,

(2, 2)

$(2, 2)$ ,

(3, 0)

$(3, 0)$

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{| 1 (B_{y} - C_{y}) + B_{x} (C_{y} - 1) + C_{x} (1 - B_{y}) |}{2}

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

Step 2.2

Substitute the values of the second point into the formula.

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

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

Step 2.3

Substitute the values of the final point into the formula.

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

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

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

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply

2 + 0

$2 + 0$ by

1

$1$ .

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

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

Step 3.2

Add

2

$2$ and

0

$0$ .

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

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

Step 3.3

Subtract

1

$1$ from

0

$0$ .

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

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

Step 3.4

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

Step 3.5

Multiply

- 1

$- 1$ by

2

$2$ .

\frac{| 2 - 2 + 3 (1 - 2) |}{2}

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

Step 3.6

Subtract

2

$2$ from

1

$1$ .

\frac{| 2 - 2 + 3 \cdot - 1 |}{2}

$\frac{| 2 - 2 + 3 \cdot - 1 |}{2}$

Step 3.7

Multiply

3

$3$ by

- 1

$- 1$ .

\frac{| 2 - 2 - 3 |}{2}

$\frac{| 2 - 2 - 3 |}{2}$

Step 3.8

Subtract

2

$2$ from

2

$2$ .

\frac{| 0 - 3 |}{2}

$\frac{| 0 - 3 |}{2}$

Step 3.9

Subtract

3

$3$ from

0

$0$ .

\frac{| - 3 |}{2}

$\frac{| - 3 |}{2}$

Step 3.10

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

- 3

$- 3$ and

0

$0$ is

3

$3$ .

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$

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