Precalculus Examples

$(- 4, - 1)$ , $(4, 1)$

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.

$\sqrt{{(4 - (- 4))}^{2} + {(1 - (- 1))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 4$ .

$\sqrt{{(4 + 4)}^{2} + {(1 - (- 1))}^{2}}$

Step 3.2

Add $4$ and $4$ .

$\sqrt{8^{2} + {(1 - (- 1))}^{2}}$

Step 3.3

Raise $8$ to the power of $2$ .

$\sqrt{64 + {(1 - (- 1))}^{2}}$

Step 3.4

Multiply $- 1$ by $- 1$ .

$\sqrt{64 + {(1 + 1)}^{2}}$

Step 3.5

Add $1$ and $1$ .

$\sqrt{64 + 2^{2}}$

Step 3.6

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

$\sqrt{64 + 4}$

Step 3.7

Add $64$ and $4$ .

$\sqrt{68}$

Step 3.8

Rewrite $68$ as $2^{2} \cdot 17$ .

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Step 3.8.1

Factor $4$ out of $68$ .

$\sqrt{4 (17)}$

Step 3.8.2

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

$\sqrt{2^{2} \cdot 17}$

Step 3.9

Pull terms out from under the radical.

$2 \sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{17}$

Decimal Form:

$8.24621125 \dots$

Step 5