Finite Math Examples

$(- 5, 1)$ , $(3, 11)$

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.

$\sqrt{{(3 - (- 5))}^{2} + {(11 - 1)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 5$ .

$\sqrt{{(3 + 5)}^{2} + {(11 - 1)}^{2}}$

Step 3.2

Add $3$ and $5$ .

$\sqrt{8^{2} + {(11 - 1)}^{2}}$

Step 3.3

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

$\sqrt{64 + {(11 - 1)}^{2}}$

Step 3.4

Subtract $1$ from $11$ .

$\sqrt{64 + 10^{2}}$

Step 3.5

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

$\sqrt{64 + 100}$

Step 3.6

Add $64$ and $100$ .

$\sqrt{164}$

Step 3.7

Rewrite $164$ as $2^{2} \cdot 41$ .

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Step 3.7.1

Factor $4$ out of $164$ .

$\sqrt{4 (41)}$

Step 3.7.2

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

$\sqrt{2^{2} \cdot 41}$

Step 3.8

Pull terms out from under the radical.

$2 \sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{41}$

Decimal Form:

$12.80624847 \dots$

Step 5