Precalculus Examples

$(- 7, 7)$ , $(3, 9)$

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.

$\sqrt{{(3 - (- 7))}^{2} + {(9 - 7)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 7$ .

$\sqrt{{(3 + 7)}^{2} + {(9 - 7)}^{2}}$

Step 3.2

Add $3$ and $7$ .

$\sqrt{10^{2} + {(9 - 7)}^{2}}$

Step 3.3

Raise $10$ to the power of $2$ .

$\sqrt{100 + {(9 - 7)}^{2}}$

Step 3.4

Subtract $7$ from $9$ .

$\sqrt{100 + 2^{2}}$

Step 3.5

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

$\sqrt{100 + 4}$

Step 3.6

Add $100$ and $4$ .

$\sqrt{104}$

Step 3.7

Rewrite $104$ as $2^{2} \cdot 26$ .

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Step 3.7.1

Factor $4$ out of $104$ .

$\sqrt{4 (26)}$

Step 3.7.2

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

$\sqrt{2^{2} \cdot 26}$

Step 3.8

Pull terms out from under the radical.

$2 \sqrt{26}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{26}$

Decimal Form:

$10.19803902 \dots$

Step 5

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