Precalculus Examples

$(- 4, 6)$ , $(3, 7)$

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.

$\sqrt{{(3 - (- 4))}^{2} + {(7 - 6)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 4$ .

$\sqrt{{(3 + 4)}^{2} + {(7 - 6)}^{2}}$

Step 3.2

Add $3$ and $4$ .

$\sqrt{7^{2} + {(7 - 6)}^{2}}$

Step 3.3

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(7 - 6)}^{2}}$

Step 3.4

Subtract $6$ from $7$ .

$\sqrt{49 + 1^{2}}$

Step 3.5

One to any power is one.

$\sqrt{49 + 1}$

Step 3.6

Add $49$ and $1$ .

$\sqrt{50}$

Step 3.7

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 3.7.1

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Step 3.7.2

Rewrite $25$ as $5^{2}$ .

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

Step 3.8

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

Step 5