P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) are the g | vedclass

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(C) The distance formula between two points $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ is given by $PQ = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}$.If

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

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(C) The distance formula between two points $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ is given by $PQ = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}$.If the line segment $\overline{PQ}$ is parallel to the $X$-axis,the $y$-coordinates of both points must be equal,i.e.,$y_{1} = y_{2}$.Substituting $y_{1} = y_{2}$ into the distance formula:$PQ = \sqrt{(x_{2} - x_{1})^2 + (y_{1} - y_{1})^2}$$PQ = \sqrt{(x_{2} - x_{1})^2 + 0^2}$$PQ = \sqrt{(x_{2} - x_{1})^2} = |x_{2} - x_{1}| = |x_{1} - x_{2}|$.Thus,the distance is $|x_{1} - x_{2}|$.

$P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ are the given points. If $\overline{PQ}$ is parallel to the $X$-axis,then $PQ = \dots$

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