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Standard XII

Mathematics

Condition for Two Lines to Be Parallel

Find the dist...

Question

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

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Solution

$P (x_{1}, y_{1}), Q (x_{2}, y_{2})$
If PQ $| |$ y axis, they have abscissa as constant.
$∴ P Q = | y_{1} - y_{2} |$
If PQ $| |$ x axis, they have ordinates as constant.
$∴ P Q = | x_{1} - x_{2} |$ .

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$Find the distance between P (x_{1}, y_{1}) a n d Q (x_{2}, y_{2}) w h e n (i) P Q i s p a r a l l e l t o t h e y - a x i x . (i i) P Q i s p a r a l l e l t o t h e x - a x i s .$

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Find the distance between P(x1,y1) and Q(xyy2) when: (i) PQ is parallel to the y -axis, (ii) PQ is parallel to the x -axis.

P(x1,y1),Q(x2,y2)If PQ||y axis, they have abscissa as constant.∴PQ=|y1−y2|If PQ||x axis, they have ordinates as constant.∴PQ=|x1−x2|.

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

$P (x_{1}, y_{1}), Q (x_{2}, y_{2})$
If PQ $| |$ y axis, they have abscissa as constant.
$∴ P Q = | y_{1} - y_{2} |$
If PQ $| |$ x axis, they have ordinates as constant.
$∴ P Q = | x_{1} - x_{2} |$ .