Question

The foot of the perpendicular from P(-3,2) to Y-axis is M. Coordinates of M are .....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) (3, 0)
(b) (0, 2)
(c) (3/2,-1)
(d) (-3, 2)

Answer 1

The foot of perpendicular from P(-3, 2) to Y-axis is M.
we know,product of slope of two perpendicular lines = -1
slope of MP × slope of Y-axis = -1

Let M = (x, y)
slope of MP = (y - 2)/(x + 3)
slope of Y - axis = 1/0
now, (y - 2)/(x + 3) × 1/0 = -1
(y - 2) × 1 = -1 × (x + 3) × 0
y - 2 = 0
y = 2
hence, point M = (x , 2) where $x\in R$
therefore, (b) and (d) both are correct.

Answer 2

According to the problem given ,

Coordinates of P ( -3 , 2 )

PM is perpendicular to Y - axis .

PM intersects Y - axis at M.

coordinates of M ( 0 , 2 )

Therefore ,

Option ( b ) is correct.

I hope this helps you.

: )