Find the Distance Between Two Points (-6,-2) , (-10,-7)

$(- 6, - 2)$ , $(- 10, - 7)$

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.

$\sqrt{{((- 10) - (- 6))}^{2} + {((- 7) - (- 2))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(- 10 + 6)}^{2} + {((- 7) - (- 2))}^{2}}$

Add $- 10$ and $6$ .

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

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

$\sqrt{16 + {((- 7) - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{16 + {(- 7 + 2)}^{2}}$

Add $- 7$ and $2$ .

$\sqrt{16 + {(- 5)}^{2}}$

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

$\sqrt{16 + 25}$

Add $16$ and $25$ .

$\sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$

Step 5