Find the Distance Between Two Points (-2,3) , (5,-3)

$(- 2, 3)$ , $(5, - 3)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $5$ and $2$ .

$\sqrt{7^{2} + {((- 3) - 3)}^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + {((- 3) - 3)}^{2}}$

Subtract $3$ from $- 3$ .

$\sqrt{49 + {(- 6)}^{2}}$

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

$\sqrt{49 + 36}$

Add $49$ and $36$ .

$\sqrt{85}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{85}$

Decimal Form:

$9.21954445 \dots$

Step 5