Algebra Examples

$(- 8, - 2)$ , $(4, - 4)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(4 - (- 8))}^{2} + {((- 4) - (- 2))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 8$ .

$\sqrt{{(4 + 8)}^{2} + {((- 4) - (- 2))}^{2}}$

Step 3.2

Add $4$ and $8$ .

$\sqrt{12^{2} + {((- 4) - (- 2))}^{2}}$

Step 3.3

Raise $12$ to the power of $2$ .

$\sqrt{144 + {((- 4) - (- 2))}^{2}}$

Step 3.4

Multiply $- 1$ by $- 2$ .

$\sqrt{144 + {(- 4 + 2)}^{2}}$

Step 3.5

Add $- 4$ and $2$ .

$\sqrt{144 + {(- 2)}^{2}}$

Step 3.6

Raise $- 2$ to the power of $2$ .

$\sqrt{144 + 4}$

Step 3.7

Add $144$ and $4$ .

$\sqrt{148}$

Step 3.8

Rewrite $148$ as $2^{2} \cdot 37$ .

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Step 3.8.1

Factor $4$ out of $148$ .

$\sqrt{4 (37)}$

Step 3.8.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 37}$

Step 3.9

Pull terms out from under the radical.

$2 \sqrt{37}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{37}$

Decimal Form:

$12.16552506 \dots$

Step 5