Find the Distance Between Two Points (0,1) and (-5,7)

$(0, 1)$ and $(- 5, 7)$

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.

$\sqrt{{((- 5) - 0)}^{2} + {(7 - 1)}^{2}}$

Step 3

Simplify.

Subtract $0$ from $- 5$ .

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

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

$\sqrt{25 + {(7 - 1)}^{2}}$

Subtract $1$ from $7$ .

$\sqrt{25 + 6^{2}}$

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

$\sqrt{25 + 36}$

Add $25$ and $36$ .

$\sqrt{61}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{61}$

Decimal Form:

$7.81024967 \dots$

Step 5