Find the Distance Between Two Points (2,1) , (8,7)

$(2, 1)$ , $(8, 7)$

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.

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

Step 3

Simplify.

Subtract $2$ from $8$ .

$\sqrt{6^{2} + {(7 - 1)}^{2}}$

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

$\sqrt{36 + {(7 - 1)}^{2}}$

Subtract $1$ from $7$ .

$\sqrt{36 + 6^{2}}$

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

$\sqrt{36 + 36}$

Add $36$ and $36$ .

$\sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Step 5