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

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

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.

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

Step 3

Simplify.

Subtract $2$ from $9$ .

$\sqrt{7^{2} + {(8 - 1)}^{2}}$

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

$\sqrt{49 + {(8 - 1)}^{2}}$

Subtract $1$ from $8$ .

$\sqrt{49 + 7^{2}}$

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

$\sqrt{49 + 49}$

Add $49$ and $49$ .

$\sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

Step 5