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

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

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.

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

Step 3

Simplify.

Subtract $1$ from $- 5$ .

$\sqrt{{(- 6)}^{2} + {(8 - 5)}^{2}}$

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

$\sqrt{36 + {(8 - 5)}^{2}}$

Subtract $5$ from $8$ .

$\sqrt{36 + 3^{2}}$

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

$\sqrt{36 + 9}$

Add $36$ and $9$ .

$\sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Step 5