Find the Distance Between Two Points (10,9) , (5,4)

$(10, 9)$ , $(5, 4)$

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.

$\sqrt{{(5 - 10)}^{2} + {(4 - 9)}^{2}}$

Step 3

Simplify.

Subtract $10$ from $5$ .

$\sqrt{{(- 5)}^{2} + {(4 - 9)}^{2}}$

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

$\sqrt{25 + {(4 - 9)}^{2}}$

Subtract $9$ from $4$ .

$\sqrt{25 + {(- 5)}^{2}}$

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

$\sqrt{25 + 25}$

Add $25$ and $25$ .

$\sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

Step 5