Find the Distance Between Two Points (3,-6) and (-1,1)

$(3, - 6)$ and $(- 1, 1)$

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.

$\sqrt{{((- 1) - 3)}^{2} + {(1 - (- 6))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $- 1$ .

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

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

$\sqrt{16 + {(1 - (- 6))}^{2}}$

Multiply $- 1$ by $- 6$ .

$\sqrt{16 + {(1 + 6)}^{2}}$

Add $1$ and $6$ .

$\sqrt{16 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{16 + 49}$

Add $16$ and $49$ .

$\sqrt{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{65}$

Decimal Form:

$8.06225774 \dots$

Step 5