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

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

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.

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

Step 3

Simplify.

Subtract $8$ from $1$ .

$\sqrt{{(- 7)}^{2} + {(1 - (- 5))}^{2}}$

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

$\sqrt{49 + {(1 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{49 + {(1 + 5)}^{2}}$

Add $1$ and $5$ .

$\sqrt{49 + 6^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{49 + 36}$

Add $49$ and $36$ .

$\sqrt{85}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{85}$

Decimal Form:

$9.21954445 \dots$

Step 5