Find the Distance Between Two Points (-5,-1) and (2,8)

$(- 5, - 1)$ and $(2, 8)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

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

Add $2$ and $5$ .

$\sqrt{7^{2} + {(8 - (- 1))}^{2}}$

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

$\sqrt{49 + {(8 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{49 + {(8 + 1)}^{2}}$

Add $8$ and $1$ .

$\sqrt{49 + 9^{2}}$

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

$\sqrt{49 + 81}$

Add $49$ and $81$ .

$\sqrt{130}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{130}$

Decimal Form:

$11.40175425 \dots$

Step 5