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Coordinate Geometry MCQs with Detailed Solutions – Level 3

Advanced coordinate geometry practice on section formula ratios, centroid and midpoint vertices, collinearity, quadrilateral area, and equations of medians and perpendicular bisectors.

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Questions, answer key and solutions.

Questions
50
Duration
75 min
Marks
50

Negative marking

Attempts
100
Access
Free
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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 75-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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

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  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
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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. 75 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.
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About this test

Coordinate Geometry Level 3 Practice Quiz: Section Formula, Area and Lines

Coordinate Geometry Level 3 on Aptitude360 is an advanced practice set on points, lines and triangles in the Cartesian plane. It covers section formula ratios, centroids and midpoints, collinearity, areas of triangles and quadrilaterals, and equations of medians and perpendicular bisectors. Every question comes with a worked solution.

Topics covered in this Coordinate Geometry Level 3 set

  • Distance formula, equidistant points and unknown coordinates from a given distance
  • The ratio in which an axis or a given line divides a segment
  • Recovering a missing vertex from the centroid or midpoints of a triangle or parallelogram
  • Areas of triangles and quadrilaterals, and collinearity of three points
  • Slopes of parallel and perpendicular lines, and the angle a line makes with the x-axis
  • Line equations from intercepts, medians, perpendicular bisectors and intersecting lines
  • Reflections in the axes and the origin, and the circumradius of a triangle

Key coordinate geometry formulas to remember

  • Distance: \( d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \)
  • Section formula, ratio m : n (y likewise): \( x=\dfrac{mx_{2}+nx_{1}}{m+n} \)
  • Centroid x-coordinate (y likewise): \( \bar{x}=\dfrac{x_{1}+x_{2}+x_{3}}{3} \)
  • Triangle area with one vertex at the origin: \( \dfrac{1}{2}\left|x_{1}y_{2}-x_{2}y_{1}\right| \)
  • Slope: \( m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} \), where \( x_{1}\neq x_{2} \)
  • Perpendicular lines, both slopes defined: \( m_{1}m_{2}=-1 \)

Revision tips for harder coordinate geometry problems

  • For the ratio in which a line divides a segment, take the ratio as k to one and substitute the point of division into the line's equation.
  • Test collinearity by setting the triangle area to zero, which also works when a line is vertical.
  • In a parallelogram the diagonals bisect each other, so equate their midpoints to find the fourth vertex.

Who this Level 3 set is for

This set suits students who are comfortable with basic coordinate geometry and want harder multi-step practice for the quantitative aptitude sections of competitive exams.

FAQs about Coordinate Geometry MCQs with Detailed Solutions – Level 3

What is the section formula in coordinate geometry?
Suppose a point divides the segment joining two points internally in the ratio m to n. Its x-coordinate is m times the second x plus n times the first x, divided by m plus n. The y-coordinate is found the same way.
How do you check if three points are collinear in coordinate geometry?
Three points are collinear if the area of the triangle they form is zero. You can also compare the slope between the first two points with the slope between the last two, but if those segments are vertical the slopes are undefined, so check instead whether all three points share the same x-coordinate.
How do you find the centroid of a triangle from its vertices?
The centroid's x-coordinate is the average of the three x-coordinates, and its y-coordinate is the average of the three y-coordinates. The centroid divides each median in the ratio two to one, measured from the vertex.
What is the condition for two lines to be perpendicular in coordinate geometry?
Two lines with defined slopes are perpendicular when the product of their slopes is minus one. A horizontal line and a vertical line are also perpendicular, even though the vertical line has no defined slope.

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 35075 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.

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