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Question
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
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Solution
- We are given that co-ordinates of P is (x1, y1) and Q is (x2 Y2)·
Distance between the points P(x1, y1) and Q (x2 y2) is
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)` ...(1)
When PQ is parallel to y-axis then x1 = x2 from (1), we have
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((x_1 - x_1)^2 + (y_2 - y_1)^2) = |y_2 - y_1|` - When PQ is parallel to x-axis, then y1 = y2 from (1), we have
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((x_2 - x_1)^2 +0) = |x_2 - x_1|`
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