Basic Math Examples

$(3, \frac{9}{2})$ , $(- 1, - \frac{7}{2})$

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.

$\sqrt{{((- 1) - 3)}^{2} + {((- \frac{7}{2}) - \frac{9}{2})}^{2}}$

Step 3

Simplify.

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Step 3.1

Simplify the expression.

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Step 3.1.1

Subtract $3$ from $- 1$ .

$\sqrt{{(- 4)}^{2} + {((- \frac{7}{2}) - \frac{9}{2})}^{2}}$

Step 3.1.2

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

$\sqrt{16 + {((- \frac{7}{2}) - \frac{9}{2})}^{2}}$

Step 3.2

Combine the numerators over the common denominator.

$\sqrt{16 + {(\frac{- 7 - 9}{2})}^{2}}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Subtract $9$ from $- 7$ .

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

Step 3.3.2

Divide $- 16$ by $2$ .

$\sqrt{16 + {(- 8)}^{2}}$

Step 3.3.3

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

$\sqrt{16 + 64}$

Step 3.3.4

Add $16$ and $64$ .

$\sqrt{80}$

Step 3.4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 3.4.1

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Step 3.4.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Step 3.5

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

Step 5