Distance

Geometry Level 1

Find the distance between the two points, ( 2 3 , − 1 3 ) \left (\dfrac{2}{3}, \dfrac{-1}{3}\right ) and ( 5 6 , − 1 2 ) \left (\dfrac{5}{6}, \dfrac{-1}{2}\right) .

Try these mixed math problems

1 6 \frac{\sqrt{1}}{6} 2 6 \frac{\sqrt{2}}{6} 2 6 \frac{\sqrt{2}}{\sqrt{6}} 2 36 \frac{\sqrt{2}}{36}

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1 solution

By using the distance formula ,

d = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 \large d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}

d = ( 5 6 − 2 3 ) 2 + ( − 1 2 + 1 3 ) 2 \large d = \sqrt{(\frac{5}{6}-\frac{2}{3})^2+(\frac{-1}{2}+\frac{1}{3})^2}

d = ( 1 6 ) 2 + ( − 1 6 ) 2 \large d = \sqrt{(\frac{1}{6})^2+(\frac{-1}{6})^2}

d = 1 36 + 1 36 \large d = \sqrt{\frac{1}{36}+\frac{1}{36}}

d = 2 36 \large d = \sqrt{\frac{2}{36}}

d = 2 36 \large d = \frac{\sqrt{2}}{\sqrt{36}}

d = 2 6 \large \color{#D61F06}\boxed{d = \frac{\sqrt{2}}{6}}

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