Find the Distance Between Two Points (7/8,-1/8) , (-1/8,7/8)

$(\frac{7}{8}, - \frac{1}{8})$ , $(- \frac{1}{8}, \frac{7}{8})$

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.

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

Step 3

Simplify.

Combine the numerators over the common denominator.

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

Simplify the expression.

Subtract $7$ from $- 1$ .

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

Divide $- 8$ by $8$ .

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

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

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

Multiply $- (- \frac{1}{8})$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{8}$ by $1$ .

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Add $7$ and $1$ .

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

Divide $8$ by $8$ .

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

One to any power is one.

$\sqrt{1 + 1}$

Add $1$ and $1$ .

$\sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Step 5