Precalculus Examples

$(2, - 1)$ , $(3, 1)$

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.

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

Step 3

Simplify.

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Step 3.1

Subtract $2$ from $3$ .

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

Step 3.2

One to any power is one.

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

Step 3.3

Multiply $- 1$ by $- 1$ .

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

Step 3.4

Add $1$ and $1$ .

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

Step 3.5

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

$\sqrt{1 + 4}$

Step 3.6

Add $1$ and $4$ .

$\sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

Step 5