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Find the Distance Between P (X1, Y1) and Q (X2, Y2) When (I) Pq is Parallel to the Y-axis (Ii) Pq is Parallel to the X-axis. - Mathematics

Sum

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

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Solution

The given points are \[P\left( x_1 , y_1 \right)\text{ and }Q\left( x_2 , y_2 \right)\]
Distance between P and Q is: \[PQ = \sqrt{\left( x_1 - x_2 \right)^2 + \left( y_1 - y_2 \right)^2}\]
(i) When PQ is parallel to the y-axis: In this case, \[x_1 = x_2\]

\[\therefore PQ = \sqrt{\left( x_1 - x_1 \right)^2 + \left( y_1 - y_2 \right)^2} = \left| y_1 - y_2 \right|\]
(ii) When PQ is parallel to the x-axis:

In this case, \[y_1 = y_2\]

\[\therefore PQ = \sqrt{\left( x_1 - x_2 \right)^2 + \left( y_1 - y_1 \right)^2} = \left| x_1 - x_2 \right|\]
Concept: Brief Review of Cartesian System of Rectanglar Co-ordinates
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 22 Brief review of cartesian system of rectangular co-ordinates
Exercise 22.1 | Q 7 | Page 13
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