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

The perpendicular is drawn from the origin. It meets the line y=mx+c at ( −1,2 ) .

The end points of the perpendicular are ( 0,0 ) and ( −1,2 ) .

The formula for the slope of a line passes through points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

m= y 2 − y 1 x 2 − x 1 (1)

Let m 1 be the slope of the perpendicular which passes through the points ( 0,0 ) and ( −1,2 ) .

Substitute the value of ( x 1 , y 1 ) and ( x 2 , y 2 ) as ( 0,0 ) and ( −1,2 ) respectively in equation (1).

m 1 = 2−0 −1−0 =−2 (2)

Let m 2 be the slope of the line.

The product of the slope of two lines perpendicular to each other is −1 .

m 1 ⋅ m 2 =−1 (3)

Substitute the value of m 1 from equation (2) to equation (3) respectively.

−2⋅ m 2 =−1 m 2 = −1 −2 = 1 2

As the point ( −1,2 ) lies on the line y=mx+c so it satisfies the equation of the line.

2=−m+c (4)

Substitute the value of m= 1 2 in equation (4).

2=− 1 2 +c c=2+ 1 2 c= 5 2

Thus the respective values for m and c are 1 2 and 5 2 .