Skip to content
Book Free Demo

Coordinate Geometry MCQs with Detailed Solutions – Level 2

Medium-level coordinate geometry MCQs on the section formula, centroid, area, collinearity, slopes and equations of lines, with a worked solution for every problem.

Start Test

Choose Normal practice or a Simulated test.

Questions, answer key and solutions.

Questions
50
Duration
60 min
Marks
50

Negative marking

Attempts
100
Access
Free
Share test:

Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 60-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

Open Normal practiceTake the Simulated test
How the two modes differ
No account needed

Normal

Untimed

Every question on one page, loading as you scroll. Choose an option and see straight away whether it was right.

  • No timer. Nothing to start and nothing to submit. Stop whenever you like.
  • Answered as you choose. Tap an option and it is marked at once, with the correct answer shown.
  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
  • Open to guests. Normal practice needs no sign-in.
Real exam conditions

Simulated

Timed CBT

The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 60 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
  • Question palette. Answered, not answered and marked for review, section by section, as the real interface has it.
  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
  • Answers hidden until you submit. The key, the explanations and your score all arrive together at the end.

About this test

Coordinate Geometry Level 2 MCQs: Section Formula, Centroid and Lines

This Level 2 coordinate geometry MCQ set on Aptitude360 is for learners who have finished the basic formulas and want medium-level, multi-step practice. It covers the distance, section and midpoint formulas, centroid, area, collinearity, slopes and equations of straight lines. Every question has a worked solution.

Topics covered in this coordinate geometry set

  • Distance formula, perimeter of a triangle and points on an axis equidistant from two given points
  • Section formula, and the ratio in which an axis or a given point divides a segment
  • Midpoint and centroid, missing vertices and the length of a median
  • Area of triangles and quadrilaterals, and collinearity of points
  • Slope, angle of inclination, and parallel and perpendicular lines
  • Equations of lines, intercepts and the triangle a line forms with the axes
  • Reflections in the axes and the origin, and vertices of a parallelogram

Key coordinate geometry formulas to revise

  • Distance: \( d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \)
  • Internal division in ratio \( m:n \), x-coordinate: \( x=\dfrac{mx_{2}+nx_{1}}{m+n} \)
  • Centroid, x-coordinate: \( x=\dfrac{x_{1}+x_{2}+x_{3}}{3} \)
  • Slope, when \( x_{1}\neq x_{2} \): \( m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} \)
  • Perpendicular lines, when both slopes are defined: \( m_{1}\times m_{2}=-1 \)
  • Intercept form: \( \dfrac{x}{a}+\dfrac{y}{b}=1 \)

Revision tips for coordinate geometry MCQs

  • To find the ratio in which the y-axis divides a segment, set the x-coordinate of the dividing point to zero; for the x-axis, set the y-coordinate to zero.
  • Three points are collinear exactly when the triangle they form has zero area.
  • The diagonals of a parallelogram bisect each other, so equate their midpoints to find unknown vertices.

Who this Level 2 set suits

It suits aptitude and school-level maths learners who know the basics and want mixed practice before moving to harder levels.

FAQs about Coordinate Geometry MCQs with Detailed Solutions – Level 2

What is the formula for the centroid of a triangle in coordinate geometry?
The centroid is found by averaging the vertices. Its x-coordinate is the sum of the three x-coordinates divided by three, and its y-coordinate is the sum of the three y-coordinates divided by three.
How do you check if three points are collinear?
Find the area of the triangle formed by the three points. If the area is zero, the points are collinear. Comparing the slopes between pairs of points also works when those slopes are defined.
What is the section formula in coordinate geometry?
The section formula gives the point that divides a line segment internally in a ratio m to n. Each coordinate equals m times the second point's coordinate plus n times the first point's coordinate, all divided by m plus n.
How do you find the midpoint of a line segment?
Add the x-coordinates of the two endpoints and halve the sum, then do the same with the y-coordinates. The midpoint is the special case of the section formula in which the ratio is one to one.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Coordinate Geometry Level 25060 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

Recommended courses for CAT & OMET

All CAT & OMET courses
Chat with an academic counsellor on WhatsApp