Find the Distance Between Two Points (6,7) and (8,2)

$(6, 7)$ and $(8, 2)$

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.

$\sqrt{{(8 - 6)}^{2} + {(2 - 7)}^{2}}$

Step 3

Simplify.

Subtract $6$ from $8$ .

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

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

$\sqrt{4 + {(2 - 7)}^{2}}$

Subtract $7$ from $2$ .

$\sqrt{4 + {(- 5)}^{2}}$

Raise $- 5$ to the power of $2$ .

$\sqrt{4 + 25}$

Add $4$ and $25$ .

$\sqrt{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{29}$

Decimal Form:

$5.38516480 \dots$

Step 5