# Find the distance between (-1/4, -1/7) and (3/4, 6/7) pair of points. If necessa

Find the distance between $$\displaystyle{\left(-\frac{1}{{4}},-\frac{1}{{7}}\right)}$$ and $$\displaystyle{\left(\frac{3}{{4}},\frac{6}{{7}}\right)}$$ pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.

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Talisha
The given two points are,
$$\displaystyle{\left(-{\frac{{{1}}}{{{4}}}},-{\frac{{{1}}}{{{7}}}}\right)}$$ and $$\displaystyle{\left({\frac{{{3}}}{{{4}}}},{\frac{{{6}}}{{{7}}}}\right)}$$
If two points are given as $$\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}$$ and $$\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}$$, then the distance between the two points is given as,
$$\displaystyle{d}=\sqrt{{{\left({x}_{{2}}-{x}_{{1}}\right)}^{{2}}+{\left({y}_{{2}}-{y}_{{1}}\right)}^{{2}}}}$$
Puting the ponts, we get
$$\displaystyle{d}=\sqrt{{{\left({\frac{{{3}}}{{{4}}}}-{\left(-{\frac{{{1}}}{{{4}}}}\right)}\right)}^{{2}}+{\left({\frac{{{6}}}{{{7}}}}-{\left(-{\frac{{{1}}}{{{7}}}}\right)}\right)}^{{2}}}}$$
$$\displaystyle=\sqrt{{{\left({\frac{{{3}+{1}}}{{{4}}}}\right)}^{{2}}+{\left({\frac{{{6}+{1}}}{{{7}}}}\right)}^{{2}}}}$$
$$\displaystyle=\sqrt{{{\left({1}\right)}^{{2}}+{\left({1}\right)}^{{2}}}}$$
$$\displaystyle=\sqrt{{{2}}}$$
$$\displaystyle={1.41}$$
Therefore, the distance between the given two points is 1.41 units.