Find the Distance Between Two Points (1,2) , (2,9)

$(1, 2)$ , $(2, 9)$

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.

$\sqrt{{(2 - 1)}^{2} + {(9 - 2)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $2$ .

$\sqrt{1^{2} + {(9 - 2)}^{2}}$

One to any power is one.

$\sqrt{1 + {(9 - 2)}^{2}}$

Subtract $2$ from $9$ .

$\sqrt{1 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{1 + 49}$

Add $1$ and $49$ .

$\sqrt{50}$

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