Find the Distance Between Two Points (-1,8) , (4,-2)

$(- 1, 8)$ , $(4, - 2)$

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.

$\sqrt{{(4 - (- 1))}^{2} + {((- 2) - 8)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(4 + 1)}^{2} + {((- 2) - 8)}^{2}}$

Add $4$ and $1$ .

$\sqrt{5^{2} + {((- 2) - 8)}^{2}}$

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

$\sqrt{25 + {((- 2) - 8)}^{2}}$

Subtract $8$ from $- 2$ .

$\sqrt{25 + {(- 10)}^{2}}$

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

$\sqrt{25 + 100}$

Add $25$ and $100$ .

$\sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

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

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

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

Step 5