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Question
Answer the following question:
Find the distance of the line 4x − y = 0 from the point P(4, 1) measured along the line making an angle of 135° with the positive X-axis
Solution
Let a line L make an angle 135° with positive X-axis.
Required distance = PQ,
where PQ || line L
Slope of PQ = tan135°
= tan(180° – 45°)
= – tan 45°
= – 1
Equation of PQ is
y – 1 = (– 1)(x – 4)
∴ y – 1 = – x + 4
∴ x + y = 5 ...(i)
To get point Q we solve the equation
4x – y = 0 with (i)
Substituting y = 4x in (i), we get
5x = 5
∴ x = 1
Substituting x = 1 in (i), we get
1 + y = 5
∴ y = 4
∴ Q = (1, 4)
PQ = `sqrt((4 - 1)^2 + (1 - 4)^2`
= `sqrt(9 + 9)`
= `3sqrt(2)`
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