Find the Distance Between Two Points (7,3) , (-2,-7)

$(7, 3)$ , $(- 2, - 7)$

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.

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

Step 3

Simplify.

Subtract $7$ from $- 2$ .

$\sqrt{{(- 9)}^{2} + {((- 7) - 3)}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{81 + {((- 7) - 3)}^{2}}$

Subtract $3$ from $- 7$ .

$\sqrt{81 + {(- 10)}^{2}}$

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

$\sqrt{81 + 100}$

Add $81$ and $100$ .

$\sqrt{181}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{181}$

Decimal Form:

$13.45362404 \dots$

Step 5