Precalculus Examples

$(- 2, 7)$ , $(3, 4)$

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.

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

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 2$ .

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

Step 3.2

Add $3$ and $2$ .

$\sqrt{5^{2} + {(4 - 7)}^{2}}$

Step 3.3

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

$\sqrt{25 + {(4 - 7)}^{2}}$

Step 3.4

Subtract $7$ from $4$ .

$\sqrt{25 + {(- 3)}^{2}}$

Step 3.5

Raise $- 3$ to the power of $2$ .

$\sqrt{25 + 9}$

Step 3.6

Add $25$ and $9$ .

$\sqrt{34}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{34}$

Decimal Form:

$5.83095189 \dots$

Step 5