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# Find the distance between P (x1, y1) and Q (x2, y2) when (ii) PQ is parallel to the x-axis.

Q : 3         Find the distance between  $P(x_1,y_1)$  and  $Q(x_2,y_2)$  when :

(ii) PQ is parallel to the $x$-axis.

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When PQ is parallel to the x-axis
then, x coordinates are equal i.e. $y_2 = y_1$
Now, we know that the distance between two points is given by
$D = |\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}|$
Now, in this case $y_2 = y_1$
Therefore,
$D = |\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}| = |\sqrt{(x_2-x_1)^2}|= |x_2-x_1|$
Therefore, the distance between $P(x_1,y_1)$ and  $Q(x_2,y_2)$  when  PQ is parallel to the x-axis  is $|x_2-x_1|$

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