Find the Distance Between Two Points (-2,6) and (7,3)

$(- 2, 6)$ and $(7, 3)$

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.

$\sqrt{{(7 - (- 2))}^{2} + {(3 - 6)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(7 + 2)}^{2} + {(3 - 6)}^{2}}$

Add $7$ and $2$ .

$\sqrt{9^{2} + {(3 - 6)}^{2}}$

Raise $9$ to the power of $2$ .

$\sqrt{81 + {(3 - 6)}^{2}}$

Subtract $6$ from $3$ .

$\sqrt{81 + {(- 3)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{81 + 9}$

Add $81$ and $9$ .

$\sqrt{90}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$\sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$3 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{10}$

Decimal Form:

$9.48683298 \dots$

Step 5