Algebra Examples

$(\frac{1}{2}, 4)$ , $(\frac{3}{2}, - 1)$

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.

$\sqrt{{(\frac{3}{2} - \frac{1}{2})}^{2} + {((- 1) - 4)}^{2}}$

Step 3

Simplify.

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Step 3.1

Combine the numerators over the common denominator.

$\sqrt{{(\frac{3 - 1}{2})}^{2} + {((- 1) - 4)}^{2}}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Subtract $1$ from $3$ .

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

Step 3.2.2

Divide $2$ by $2$ .

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

Step 3.2.3

One to any power is one.

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

Step 3.2.4

Subtract $4$ from $- 1$ .

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

Step 3.2.5

Raise $- 5$ to the power of $2$ .

$\sqrt{1 + 25}$

Step 3.2.6

Add $1$ and $25$ .

$\sqrt{26}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{26}$

Decimal Form:

$5.09901951 \dots$

Step 5