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Question
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
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Solution
Let the equation of line PC be 2x – y = 0 on which point P(1, 2) lies.
On solving the equation of line AB 4x + 7y + 5 = 0 and 2x – y = 0,
∴ x = `(-5)/18`
and y = `-5/9`
∴ The coordinates of C are `((-5)/18, (-5)/9)` which is the intersection point and the coordinates of P are (1, 2).
Required length PC = `sqrt((-5/18 - 1)^2 + ((-5)/9 - 2)^2)`
= `sqrt(((-23)/18)^2 + ((-23)/9)^2)`
= `23/9 sqrt((1/2)^2 + 1)`
= `23/9 xx sqrt5/2`
= `(23sqrt5)/18`
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