Find the Distance Between Two Points (2/7,3/2) , (4/7,3/2)

$(\frac{2}{7}, \frac{3}{2})$ , $(\frac{4}{7}, \frac{3}{2})$

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.

$\sqrt{{(\frac{4}{7} - \frac{2}{7})}^{2} + {(\frac{3}{2} - \frac{3}{2})}^{2}}$

Step 3

Simplify.

Combine the numerators over the common denominator.

$\sqrt{{(\frac{4 - 2}{7})}^{2} + {(\frac{3}{2} - \frac{3}{2})}^{2}}$

Simplify the expression.

Subtract $2$ from $4$ .

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

Apply the product rule to $\frac{2}{7}$ .

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

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

$\sqrt{\frac{4}{7^{2}} + {(\frac{3}{2} - \frac{3}{2})}^{2}}$

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

$\sqrt{\frac{4}{49} + {(\frac{3}{2} - \frac{3}{2})}^{2}}$

Combine the numerators over the common denominator.

$\sqrt{\frac{4}{49} + {(\frac{3 - 3}{2})}^{2}}$

Simplify the expression.

Subtract $3$ from $3$ .

$\sqrt{\frac{4}{49} + {(\frac{0}{2})}^{2}}$

Divide $0$ by $2$ .

$\sqrt{\frac{4}{49} + 0^{2}}$

Raising $0$ to any positive power yields $0$ .

$\sqrt{\frac{4}{49} + 0}$

Add $\frac{4}{49}$ and $0$ .

$\sqrt{\frac{4}{49}}$

Rewrite $\sqrt{\frac{4}{49}}$ as $\frac{\sqrt{4}}{\sqrt{49}}$ .

$\frac{\sqrt{4}}{\sqrt{49}}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2}}}{\sqrt{49}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{\sqrt{49}}$

Simplify the denominator.

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

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

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{7}$

Step 4