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.

Given: perpendicular from the origin and meets at the point (-1, 2)

Explanation:

The given line is y = mx + c which can be written as mx –y + c = 0 … (1)

The slope of the line perpendicular to y = mx + c is

So, the equation of the line with slope and passing through the origin is

x + my = 0 … (2)

Solving eq(1) and eq(2) by cross multiplication, we get

Thus, the point of intersection of the perpendicular from the origin to the line y = mx + c is

It is given that the perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2)

and

⇒ m² + 1 = mc and m² + 1

⇒ mc

⇒ m

Now, substituting the value of m in m² + 1 = mc, we get

⇒ c

Hence, m and c