Find the Distance Between Two Points (-5,6) and (-3,-1)

$(- 5, 6)$ and $(- 3, - 1)$

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.

$\sqrt{{((- 3) - (- 5))}^{2} + {((- 1) - 6)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 3 + 5)}^{2} + {((- 1) - 6)}^{2}}$

Add $- 3$ and $5$ .

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

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

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

Subtract $6$ from $- 1$ .

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

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

$\sqrt{4 + 49}$

Add $4$ and $49$ .

$\sqrt{53}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{53}$

Decimal Form:

$7.28010988 \dots$

Step 5