Find the distance between the points

Question:

Find the distance between the points $\left(\frac{-8}{5}, 2\right)$ and $\left(\frac{2}{5}, 2\right)$.

 

Solution:

The given points are $A\left(\frac{-8}{5}, 2\right)$ and $B\left(\frac{2}{5}, 2\right)$.

Then, $\left(x_{1}=\frac{-8}{5}, y_{1}=2\right)$ and $\left(x_{2}=\frac{2}{5}, y_{2}=2\right)$

Therefore,

$A B=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

$=\sqrt{\left\{\frac{2}{5}-\left(\frac{-8}{5}\right)\right\}^{2}+(2-2)^{2}}$

$=\sqrt{(2)^{2}+(0)^{2}}$

$=\sqrt{4+0}$

$=\sqrt{4}$

$=2$ units

 

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