Precalculus Examples

$(- 5, 2)$ , $(7, - 3)$

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.

$\sqrt{{(7 - (- 5))}^{2} + {((- 3) - 2)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 5$ .

$\sqrt{{(7 + 5)}^{2} + {((- 3) - 2)}^{2}}$

Step 3.2

Add $7$ and $5$ .

$\sqrt{12^{2} + {((- 3) - 2)}^{2}}$

Step 3.3

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

$\sqrt{144 + {((- 3) - 2)}^{2}}$

Step 3.4

Subtract $2$ from $- 3$ .

$\sqrt{144 + {(- 5)}^{2}}$

Step 3.5

Raise $- 5$ to the power of $2$ .

$\sqrt{144 + 25}$

Step 3.6

Add $144$ and $25$ .

$\sqrt{169}$

Step 3.7

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}}$

Step 3.8

Pull terms out from under the radical, assuming positive real numbers.

$13$

Step 4