How Many Different Lines Are Determined by 4 Distinct Points in a Plane If No 3 GMAT Problem Solving

Question: How many different lines are determined by 4 distinct points in a plane if no 3 of the points lie on the same straight line?

1. 4
2. 5
3. 6
4. 7
5. 12

‘How many different lines are determined by 4 distinct points in a plane if no 3 of the points lie on the same straight line?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review".
To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

This question has only one approach.
It is asked in the question that how many different lines are determined by 4 distinct points in a plane if no 3 of the points lie on the same straight line.
This is a question from coordinate geometry.
We know that two points are required to form a line.
There are 4 distinct points in a plane, the number of lines which can be made from these points = 4C2 = 4!/(2! 2!) = 4*3/(2) = 6
There can be 6 different lines determined by 4 distinct points in a plane of no 3 of the points lying on the same straight line.
The correct option will be option C.
Correct Answer: C

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