Find the Distance Between Two Points (1,3) , (-7,2)

$(1, 3)$ , $(- 7, 2)$

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.

$\sqrt{{((- 7) - 1)}^{2} + {(2 - 3)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $- 7$ .

$\sqrt{{(- 8)}^{2} + {(2 - 3)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{64 + {(2 - 3)}^{2}}$

Subtract $3$ from $2$ .

$\sqrt{64 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{64 + 1}$

Add $64$ and $1$ .

$\sqrt{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{65}$

Decimal Form:

$8.06225774 \dots$

Step 5