Sum

Find the distance between P (x_{1}, y_{1}) and Q (x_{2}, y_{2}) 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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