A 2 minute read

In a rectangular coordinate system, straight-line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k? – OGQR 2020 Question #78 with Solution

OGQR 2020: Question No. 78

In a rectangular coordinate system, straight-line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k?

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicCoordinate Geometry
DifficultyEasy-Medium

Solution

Given

In this question, we are given

  • In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2).

To Find

We need to determine

  • Among the given choices, which one indicates the coordinates of a point on k.

Approach & Working

As we know that straight line k passes through points (0, 0) and (3, 2), the equation of the line k must be

  • y – 0 / x – 0 = 0-2 / 0 -3

Or,  y/x = 2/3

Or, 2x = 3y

Now, if a point is on the line k, it should satisfy the equation of the line.

Checking with the given options:

  • (9, 4): 2x = 2 * 9 = 18 & 3y = 3 * 4 = 12, hence, 2x ≠ 3y
  • (4, 9): 2x = 2 * 4 = 8 & 3y = 3 * 9 = 27, hence, 2x ≠ 3y
  • (-4, 6): 2x = 2 * -4 = -8 & 3y = 3 * 6 = 18, hence, 2x ≠ 3y
  • (-6, -9): 2x = 2 * -6 = -12 & 3y = 3 * -9 = -27, hence, 2x ≠ 3y
  • (-6, -4): 2x = 2 * -6 = -12 & 3y = 3 * -4 = -12, hence, 2x = 3y

Hence, the correct answer is option E.

Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you try out our FREE Trial? We are the most reviewed online GMAT Preparation company in GMATClub with more than 2000 reviews as of July 2021.

People who read this article also read

Let's discuss further - What's your take?

Payal Tandon
Co-founder, e-GMAT
Welcome to e-GMAT Support!
I am Payal, Co-Founder of e-GMAT.
Feel free to ask any Query.
Thank you for your query.
We will be contacting you soon on