Find the Distance Between Two Points (2,-8) , (9,-5)

$(2, - 8)$ , $(9, - 5)$

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.

$\sqrt{{(9 - 2)}^{2} + {((- 5) - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $2$ from $9$ .

$\sqrt{7^{2} + {((- 5) - (- 8))}^{2}}$

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

$\sqrt{49 + {((- 5) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{49 + {(- 5 + 8)}^{2}}$

Add $- 5$ and $8$ .

$\sqrt{49 + 3^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{49 + 9}$

Add $49$ and $9$ .

$\sqrt{58}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{58}$

Decimal Form:

$7.61577310 \dots$

Step 5