Pre-Algebra Examples

$(1, 5)$ , $(7, 11)$

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.

$\sqrt{{(7 - 1)}^{2} + {(11 - 5)}^{2}}$

Step 3

Simplify.

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Step 3.1

Subtract $1$ from $7$ .

$\sqrt{6^{2} + {(11 - 5)}^{2}}$

Step 3.2

Raise $6$ to the power of $2$ .

$\sqrt{36 + {(11 - 5)}^{2}}$

Step 3.3

Subtract $5$ from $11$ .

$\sqrt{36 + 6^{2}}$

Step 3.4

Raise $6$ to the power of $2$ .

$\sqrt{36 + 36}$

Step 3.5

Add $36$ and $36$ .

$\sqrt{72}$

Step 3.6

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 3.6.1

Factor $36$ out of $72$ .

$\sqrt{36 (2)}$

Step 3.6.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2}$

Step 3.7

Pull terms out from under the radical.

$6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Step 5