Find the Distance Between Two Points (10,-1) , (-6,3)

$(10, - 1)$ , $(- 6, 3)$

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.

$\sqrt{{((- 6) - 10)}^{2} + {(3 - (- 1))}^{2}}$

Step 3

Simplify.

Subtract $10$ from $- 6$ .

$\sqrt{{(- 16)}^{2} + {(3 - (- 1))}^{2}}$

Raise $- 16$ to the power of $2$ .

$\sqrt{256 + {(3 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{256 + {(3 + 1)}^{2}}$

Add $3$ and $1$ .

$\sqrt{256 + 4^{2}}$

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

$\sqrt{256 + 16}$

Add $256$ and $16$ .

$\sqrt{272}$

Rewrite $272$ as $4^{2} \cdot 17$ .

Factor $16$ out of $272$ .

$\sqrt{16 (17)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 17}$

Pull terms out from under the radical.

$4 \sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{17}$

Decimal Form:

$16.49242250 \dots$

Step 5