Find the Distance Between Two Points (4,6) , (7,-3)

$(4, 6)$ , $(7, - 3)$

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.

$\sqrt{{(7 - 4)}^{2} + {((- 3) - 6)}^{2}}$

Step 3

Simplify.

Subtract $4$ from $7$ .

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

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

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

Subtract $6$ from $- 3$ .

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

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

$\sqrt{9 + 81}$

Add $9$ and $81$ .

$\sqrt{90}$

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