Find the Distance Between Two Points (3,-5) , (-3,9)

$(3, - 5)$ , $(- 3, 9)$

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.

$\sqrt{{((- 3) - 3)}^{2} + {(9 - (- 5))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $- 3$ .

$\sqrt{{(- 6)}^{2} + {(9 - (- 5))}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {(9 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{36 + {(9 + 5)}^{2}}$

Add $9$ and $5$ .

$\sqrt{36 + 14^{2}}$

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

$\sqrt{36 + 196}$

Add $36$ and $196$ .

$\sqrt{232}$

Rewrite $232$ as $2^{2} \cdot 58$ .

Factor $4$ out of $232$ .

$\sqrt{4 (58)}$

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

$\sqrt{2^{2} \cdot 58}$

Pull terms out from under the radical.

$2 \sqrt{58}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{58}$

Decimal Form:

$15.23154621 \dots$

Step 5