Find the Distance Between Two Points (2,8) , (-1,9)

$(2, 8)$ , $(- 1, 9)$

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.

$\sqrt{{((- 1) - 2)}^{2} + {(9 - 8)}^{2}}$

Step 3

Simplify.

Subtract $2$ from $- 1$ .

$\sqrt{{(- 3)}^{2} + {(9 - 8)}^{2}}$

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

$\sqrt{9 + {(9 - 8)}^{2}}$

Subtract $8$ from $9$ .

$\sqrt{9 + 1^{2}}$

One to any power is one.

$\sqrt{9 + 1}$

Add $9$ and $1$ .

$\sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$

Step 5