Find the Distance Between Two Points (7,5) , (-4,-7)

$(7, 5)$ , $(- 4, - 7)$

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.

$\sqrt{{((- 4) - 7)}^{2} + {((- 7) - 5)}^{2}}$

Step 3

Simplify.

Subtract $7$ from $- 4$ .

$\sqrt{{(- 11)}^{2} + {((- 7) - 5)}^{2}}$

Raise $- 11$ to the power of $2$ .

$\sqrt{121 + {((- 7) - 5)}^{2}}$

Subtract $5$ from $- 7$ .

$\sqrt{121 + {(- 12)}^{2}}$

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

$\sqrt{121 + 144}$

Add $121$ and $144$ .

$\sqrt{265}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{265}$

Decimal Form:

$16.27882059 \dots$

Step 5