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Question
The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the values of m and c.
Solution
Let the equation of line AB be, y = mx + c
Slope of line AB = m
From O, perpendicular OC is drawn on line AB, which meets at point C(−1, 2).
∴ Slope of perpendicular line OC = `-1/"m"`
Now the equation of line OC,
y – 0 = `-1/"m"("x" - 0)`
or x + my = 0
Slope of OC = `(2 - 0)/(-1 -1) = -2`
Slope of perpendicular line OC = `-1/"m"`
The point C (−1, 2) lies on the following line:
y = mx + c
⇒ 2 = –m + c
Putting m = `1/2`,
2 = `- 1/2 + "c"`
∴ C = `2 + 1/2`
= `5/2`
Hence, m = `1/2`, C = `5/2`.
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