Question

Given four points such that no three of them are collinear. Then, find the number of lines that can be drawn through them.​

Answer 1

Answer:

4 lines

• Step-by-step explanation:

explained in the figure

Answer 2

Therefore '6' lines can be drawn through 4 non-collinear lines.

Given:

4 points are given such that no 3 of them are collinear.

To Find:

The number of lines that can be drawn through them.

Solution:

The given question can be solved as shown below.

Given that None of the 3 points are collinear out of 4.

The number of lines that can be drawn through them is nothing but picking up any 2 points out of '4'.

This can be done by combinations.

Let the total number of points = n = 4

Let the number of points to be chosen = a = 2

To choose 2 points out of 4 = ⁿCₐ

⇒ ⁴C₂ = 4! / 2! × ( 4 - 2 )! = ( 4 × 3 × 2× 1 ) / ( 2 × 1 ) ( 2 × 1 )

⇒ ⁴C₂ = 3 × 2 = 6

Therefore '6' lines can be drawn through 4 non-collinear lines.

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