Find the Distance Between Two Points (6,4) and (1,8)

$(6, 4)$ and $(1, 8)$

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.

$\sqrt{{(1 - 6)}^{2} + {(8 - 4)}^{2}}$

Step 3

Simplify.

Subtract $6$ from $1$ .

$\sqrt{{(- 5)}^{2} + {(8 - 4)}^{2}}$

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

$\sqrt{25 + {(8 - 4)}^{2}}$

Subtract $4$ from $8$ .

$\sqrt{25 + 4^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{25 + 16}$

Add $25$ and $16$ .

$\sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$

Step 5