Precalculus Examples

$(- 8, - 2)$ , $(- 1, - 4)$

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.

$\sqrt{{((- 1) - (- 8))}^{2} + {((- 4) - (- 2))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 8$ .

$\sqrt{{(- 1 + 8)}^{2} + {((- 4) - (- 2))}^{2}}$

Step 3.2

Add $- 1$ and $8$ .

$\sqrt{7^{2} + {((- 4) - (- 2))}^{2}}$

Step 3.3

Raise $7$ to the power of $2$ .

$\sqrt{49 + {((- 4) - (- 2))}^{2}}$

Step 3.4

Multiply $- 1$ by $- 2$ .

$\sqrt{49 + {(- 4 + 2)}^{2}}$

Step 3.5

Add $- 4$ and $2$ .

$\sqrt{49 + {(- 2)}^{2}}$

Step 3.6

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

$\sqrt{49 + 4}$

Step 3.7

Add $49$ and $4$ .

$\sqrt{53}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{53}$

Decimal Form:

$7.28010988 \dots$

Step 5