Find the Distance Between Two Points (9,-10) , (-3,4)

$(9, - 10)$ , $(- 3, 4)$

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.

$\sqrt{{((- 3) - 9)}^{2} + {(4 - (- 10))}^{2}}$

Step 3

Simplify.

Subtract $9$ from $- 3$ .

$\sqrt{{(- 12)}^{2} + {(4 - (- 10))}^{2}}$

Raise $- 12$ to the power of $2$ .

$\sqrt{144 + {(4 - (- 10))}^{2}}$

Multiply $- 1$ by $- 10$ .

$\sqrt{144 + {(4 + 10)}^{2}}$

Add $4$ and $10$ .

$\sqrt{144 + 14^{2}}$

Raise $14$ to the power of $2$ .

$\sqrt{144 + 196}$

Add $144$ and $196$ .

$\sqrt{340}$

Rewrite $340$ as $2^{2} \cdot 85$ .

Factor $4$ out of $340$ .

$\sqrt{4 (85)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 85}$

Pull terms out from under the radical.

$2 \sqrt{85}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{85}$

Decimal Form:

$18.43908891 \dots$

Step 5