Find the Distance Between Two Points (2,3) , (1,7)

$(2, 3)$ , $(1, 7)$

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.

$\sqrt{{(1 - 2)}^{2} + {(7 - 3)}^{2}}$

Step 3

Simplify.

Subtract $2$ from $1$ .

$\sqrt{{(- 1)}^{2} + {(7 - 3)}^{2}}$

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

$\sqrt{1 + {(7 - 3)}^{2}}$

Subtract $3$ from $7$ .

$\sqrt{1 + 4^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{1 + 16}$

Add $1$ and $16$ .

$\sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{17}$

Decimal Form:

$4.12310562 \dots$

Step 5