Find the Distance Between Two Points (12,11) , (5,1)

$(12, 11)$ , $(5, 1)$

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.

$\sqrt{{(5 - 12)}^{2} + {(1 - 11)}^{2}}$

Step 3

Simplify.

Subtract $12$ from $5$ .

$\sqrt{{(- 7)}^{2} + {(1 - 11)}^{2}}$

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

$\sqrt{49 + {(1 - 11)}^{2}}$

Subtract $11$ from $1$ .

$\sqrt{49 + {(- 10)}^{2}}$

Raise $- 10$ to the power of $2$ .

$\sqrt{49 + 100}$

Add $49$ and $100$ .

$\sqrt{149}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{149}$

Decimal Form:

$12.20655561 \dots$

Step 5