Find the Distance Between Two Points (11,7) , (16,6)

$(11, 7)$ , $(16, 6)$

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.

$\sqrt{{(16 - 11)}^{2} + {(6 - 7)}^{2}}$

Step 3

Simplify.

Subtract $11$ from $16$ .

$\sqrt{5^{2} + {(6 - 7)}^{2}}$

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

$\sqrt{25 + {(6 - 7)}^{2}}$

Subtract $7$ from $6$ .

$\sqrt{25 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{25 + 1}$

Add $25$ and $1$ .

$\sqrt{26}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{26}$

Decimal Form:

$5.09901951 \dots$

Step 5