Find the Distance Between Two Points (2,-1) , (1,6)

$(2, - 1)$ , $(1, 6)$

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.

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

Step 3

Simplify.

Subtract $2$ from $1$ .

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

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

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

Multiply $- 1$ by $- 1$ .

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

Add $6$ and $1$ .

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

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