Question

How many points are needed to establish a plane?

Answer 1

Hint: In order to solve this question first we need to recall the definition of a plane and then we will analyze the position of points to draw a plane. Then we will get the answer to this question.

Complete step by step answer:
We know that in mathematics a plane is a flat two-dimensional surface that spreads infinitely. The plane refers to the whole space. In mathematics many tasks like graphing, geometry, trigonometry are performed in a two-dimensional space i.e. in plane.
Now, we know that if three points are collinear i.e. not situated in one line they form a plane.
Let us consider three points A, B and C
Now, the obtained plane will be

Hence we require three collinear points to establish a plane.

Note: A plane is uniquely determined by any of the following: by three collinear points, a line and a point (point not lying on the line), two distinct and intersecting lines, two distinct but parallel lines. Two distinct planes are either parallel or they intersect in a line. A line is either parallel to a plane, intersects it at a single point or contained in a plane. Two distinct lines perpendicular to the same plane must be parallel to each other. Two distinct planes perpendicular to the same line must be parallel to each other.