Find the Distance Between Two Points (3,-8) and (-2,-1)

$(3, - 8)$ and $(- 2, - 1)$

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.

$\sqrt{{((- 2) - 3)}^{2} + {((- 1) - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $- 2$ .

$\sqrt{{(- 5)}^{2} + {((- 1) - (- 8))}^{2}}$

Raise $- 5$ to the power of $2$ .

$\sqrt{25 + {((- 1) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{25 + {(- 1 + 8)}^{2}}$

Add $- 1$ and $8$ .

$\sqrt{25 + 7^{2}}$

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

$\sqrt{25 + 49}$

Add $25$ and $49$ .

$\sqrt{74}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{74}$

Decimal Form:

$8.60232526 \dots$

Step 5