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.

Answer 1

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`.