Find the Distance Between Two Points (7,-8) , (-10,-4)

$(7, - 8)$ , $(- 10, - 4)$

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.

$\sqrt{{((- 10) - 7)}^{2} + {((- 4) - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $7$ from $- 10$ .

$\sqrt{{(- 17)}^{2} + {((- 4) - (- 8))}^{2}}$

Raise $- 17$ to the power of $2$ .

$\sqrt{289 + {((- 4) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{289 + {(- 4 + 8)}^{2}}$

Add $- 4$ and $8$ .

$\sqrt{289 + 4^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{289 + 16}$

Add $289$ and $16$ .

$\sqrt{305}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{305}$

Decimal Form:

$17.46424919 \dots$

Step 5