Find the distance between P(x_{1}, y_{1}) and | vedclass

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Question

(A) The given points are $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$.Since $PQ$ is parallel to the $x$-axis,the $y$-coordinates of both points must be equ

Vedclass · Accepted Answer

$|x_{2} - x_{1}|$

Vedclass · Answer

(A) The given points are $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$.Since $PQ$ is parallel to the $x$-axis,the $y$-coordinates of both points must be equal,i.e.,$y_{1} = y_{2}$.The distance formula is $d = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$.Substituting $y_{2} = y_{1}$ into the formula,we get $d = \sqrt{(x_{2}-x_{1})^2 + (y_{1}-y_{1})^2}$.$d = \sqrt{(x_{2}-x_{1})^2 + 0^2}$.$d = \sqrt{(x_{2}-x_{1})^2} = |x_{2}-x_{1}|$.

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $x$-axis.

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