Find the Distance Between Two Points What is the distance between the points (1,2) and (4,6) ?

What is the distance between the points $(1, 2)$ and $(4, 6)$ ?

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.

$\sqrt{{(4 - 1)}^{2} + {(6 - 2)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $4$ .

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

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

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

Subtract $2$ from $6$ .

$\sqrt{9 + 4^{2}}$

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

$\sqrt{9 + 16}$

Add $9$ and $16$ .

$\sqrt{25}$

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

$\sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5$

Step 4