Find the Distance Between Two Points (1,1) , (4,7)

$(1, 1)$ , $(4, 7)$

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.

$\sqrt{{(4 - 1)}^{2} + {(7 - 1)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $4$ .

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

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

$\sqrt{9 + {(7 - 1)}^{2}}$

Subtract $1$ from $7$ .

$\sqrt{9 + 6^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{9 + 36}$

Add $9$ and $36$ .

$\sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Step 5