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.

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The given equation of the line is y = mx + c.

From the given condition, the perpendicular from the origin meets the given line at (-1, 2).

Hence, the line joining the points (0, 0) and (-1, 2) is perpendicular to the given line.

The slope of the line joining (0, 0) and (-1, 2) is

= 2/-1 = -2

Therefore,

m (– 2) = -1 (Since the two lines are perpendicular)

m= ½

Since points (-1, 2) lies on the given line, it satisfies the equation y = mx + c.

Now, substitute the value of m, (x, y) coordinates in the equation:

2 = m(-1) + c

2 = ½(-1) + c

2 = -½ + c

C = 2 + (½)

C = 5/2

Therefore, the value of m and c are ½ and 5/2 respectively.

Thanks