Find the Distance Between Two Points (-2,5) , (-1,1)

$(- 2, 5)$ , $(- 1, 1)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $- 1$ and $2$ .

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

One to any power is one.

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

Subtract $5$ from $1$ .

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

Raise $- 4$ to the power of $2$ .

$\sqrt{1 + 16}$

Add $1$ and $16$ .

$\sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{17}$

Decimal Form:

$4.12310562 \dots$

Step 5