Algebra Examples

Find the distance between the points $(- 4, - 9)$ and $(- 8, 1)$

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.

$\sqrt{{((- 8) - (- 4))}^{2} + {(1 - (- 9))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 4$ .

$\sqrt{{(- 8 + 4)}^{2} + {(1 - (- 9))}^{2}}$

Step 3.2

Add $- 8$ and $4$ .

$\sqrt{{(- 4)}^{2} + {(1 - (- 9))}^{2}}$

Step 3.3

Raise $- 4$ to the power of $2$ .

$\sqrt{16 + {(1 - (- 9))}^{2}}$

Step 3.4

Multiply $- 1$ by $- 9$ .

$\sqrt{16 + {(1 + 9)}^{2}}$

Step 3.5

Add $1$ and $9$ .

$\sqrt{16 + 10^{2}}$

Step 3.6

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

$\sqrt{16 + 100}$

Step 3.7

Add $16$ and $100$ .

$\sqrt{116}$

Step 3.8

Rewrite $116$ as $2^{2} \cdot 29$ .

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Step 3.8.1

Factor $4$ out of $116$ .

$\sqrt{4 (29)}$

Step 3.8.2

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

$\sqrt{2^{2} \cdot 29}$

Step 3.9

Pull terms out from under the radical.

$2 \sqrt{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{29}$

Decimal Form:

$10.77032961 \dots$

Step 5