Question

Point A lies outside of plane P. How many lines can be drawn perpendicular to plane P through point A?

answers:
A) 0
B) 2
C) AN INFINITE NUMBER
D) 1

Answer 1

The correct option is D.

Explanation:

Given information: Point A lies outside of plane P.

Definition of Plane : A plane is a two-dimensional, flat surface that extends infinitely far.

Line perpendicular to a plane means, the line makes 90° angle with the plane.

Let as assume if a line passes through a point A and perpendicular to the plane P, then the number of possible lines are two.

It means line is perpendicular on two points of the plane,i.e., P₁ and P₂.

Since both line as perpendicular, therefore the length of line segment is same.

`AP_1=AP_2`

It is only possible, when

`P_1=P_2`

If a line passes through a point A and perpendicular to the plane P, then the number of possible lines is 1.

Therefore the correct option is D.

Answer 2

D) 1

Explanation

A perpendicular line makes a angle of 90° with a line or a plane.

If a line is to be drawn from a point to a line or a plain it can only be one. In this case a line is to be drawn through a point A to a plane P. If the line is to be perpendicular, then is is only one.

From the choices, the appropriate answer is D) 1