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CAT Questions | CAT Geometry Questions | Coordinate Geometry

Coordinate Geometry is one of the most important topics of Quantitative Aptitude and it comes in most of the MBA Entrance exams, like CAT, GMAT, XAT, MAT, and CMAT. In particular, it is central to the mathematics students at any school.

Common questions in CAT which assess the candidate on Coordinate Geometry concepts are related to finding the value of certain angles or length of certain sides. Therefore, topics such as Congruency and Similarity of triangles are of the utmost importance when it comes to Coordinate Geometry.

Coordinate geometry concepts basically provide a connection between algebra and geometry with the use of graphs of lines and curves. Coordinate geometry aptitude questions have been coming a lot in recent years, so this topic is very important for scoring high marks. Two to three questions every year can be expected. Moreover, it also has many uses in fields of trigonometry, calculus, dimensional geometry, and more.

Coordinate Geometry concepts can be used to find out the locations of aircrafts and pilots securing safety reasons. Also these basic concepts in geometry can be used for computer programming. Thus for candidates who wish to excel in the aircraft industry and computer programming, Coordinate Geometry is highly important.

FREQUENCY OF COORDINATE GEOMETRY QUESTIONS IN THESE ENTRANCE EXAMS

CAT

Year SLOT NO OF QUESTIONS GOOD ATTEMPT DIFFICULTY
Slot 1 2 2 Easy
Slot 2 2 2 Easy
Slot 1 2 2 Moderate
Slot 2 3 1 Difficult

XAT

YEAR NO OF QUESTIONS GOOD ATTEMPT DIFFICULTY
2020 3 2 Moderate
2019 2 1 Moderate
2018 1 1 Easy

CMAT

YEAR NO OF QUESTIONS GOOD ATTEMPT DIFFICULTY
2020 2 2 Easy
2019 3 2 Moderate
2018 4 4 Easy

MAT

YEAR NO OF QUESTIONS GOOD ATTEMPT DIFFICULTY
2019 3 2 Easy-moderate
2018 2 1 Difficult
2017 1 1 Easy

Basic concepts on Coordinate geometry

  1. 2D Geometry – For e.g. Distance formula, Section formula, Area of triangle, Locus of a point, and Transformation of taxis
  2. Geometric Probability
  3. Coordinate geometry concepts on Integer Coordinates
  4. Coordinate geometry concepts on Straight Lines
  5. Coordinate geometry concepts on Mid-Point Theorem
  6. Finding the Coordinate Plane
  7. Finding the Conic section – For e.g. sections of Circle, Parabola, Ellipse, Hyperbola and Pair of Straight lines
  8. The Distance Between two Points
  9. Finding the value of The Midpoint of a Line joining two points
  10. Finding the value of The Gradient of a Line joining two points
  11. Parallel and Perpendicular Lines
  12. Finding out the Equation of a Line using One Point and the Gradient
  13. Coordinate geometry concepts of the product of the slopes of two perpendicular lines are–1
  14. Coordinate geometry concepts of equal slopes of parallel lines
  15. Coordinate geometry concepts of Quadrants – For e.g. Quadrant I = X is positive and Y is positive, Quadrant II = X is negative and Y is positive
  16. Equations of a line – For e.g. knowing that the General equation of a line Ax + By = C

CAT Aptitude questions | CAT Geometry: Coordinate Geometry

1. 1. The area, in sq. units, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis is equal to 

              A) 10         B) 8 C) 6     D) 12                                                 

[CAT 2020]

y = |x| is a symmetric function, symmetric on the y axis…

y = |x – 2| + 4 is nothing but a translated graph of y = |x| from (0 , 0) to (2 , 4)

 

We are asked to find the area, in sq. units, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis.

 

Now the enclosed area is the sum of areas of the rectangle and the triangle.

Enclosed Area = 2 × 4 + (½) × 2 × 2 = 8 + 2 = 10

 

2. Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

A) 3:4         B) 2:3        C) 5:6       D) 4:5

[CAT 2019]

Area of the shaded region = 2*(area of one shaded region) = 2*1/2 *1*2 = 2 unit

 

3. With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is ________________.

[CAT 2019]

Dimension of rectangle with ends of diagonal being(1,1) and (4,6) = 3*5

Thus number of paths from (1,1) to (4,6) = (5+3)!/5!3! =56

Dimension of rectangle with ends of diagonal being(8,10) and (4,6) = 4*4

Thus number of paths from (4,6) to (8,10) = (4+4)!/4!4! =70

So total number of paths from (1,1) to (8,10) via (4,6) = 56*70 =3920

Ratio of their interest at the end of a year = 3*6 : 4*5 : 5*4 = 18 : 20:20

4.  the shortest distance of the point (1/2,1) from the curve y = |x -1| + |x + 1| is

a) 1         b) 0        c) √2       d) 3/√2       

[CAT 2017]   

The shortest distance of   from the graph is 1

How to deal with Coordinate Geometry preparation

LEVEL 1

1. Students are supposed to have basic knowledge of the Coordinate geometry from MBAP CAT E Book (Concept Theory) study material

2. Do not practice a single problem in coordinate geometry without drawing a figure

3. Try to memorize as many formulae as you can. Take help of live lectures.

4. Try your best to solve a problem before referring to its solution from MBAP CAT E Book (Practice Questions).

5. Follow the lecture notes. Make a different notebook for the basicgeometry formulas. Write all the important formulas of coordinate geometry in your notebook daily.

LEVEL 2

1. Mid-Point theorem is a very important coordinate geometry concept and students need to be thorough with this chapter 

2. Questions from Section formula and Distance formula can be very twisted, so students should practice these topics from MBAP Topic wise Previous Year CAT Question very carefully. Read the questions clearly to figure out what it actually demands, which would in turn save your time

LEVEL 3

Students need to be fluent with the basic concepts of coordinate geometry. Concepts of a plane, and the distances and, how coordinates are allocated. Try to answer coordinate geometry questions from the advanced level of previous cat papers, mock tests, and materials from MBAP CAT Advance E books. Finish all the concepts, examples, and questions given in Sarvesh K.Verma’s book along with miscellaneous exercises. Then you can refer to the Quantitative Aptitude book by Arun Sharma. Do not read the same concepts from different books as it will lead to confusion. Always stick to one particular book, preferably Arun Sharma. Coordinate Geometry concepts with thousands of solved examples and diagrams make the problems on geometry easy for a candidate and they will be able to perform better. If you are stuck with a coordinate geometry question, don’t waste your time trying to solve it right away. Instead, get on with the others and come back to the question when you are done with the rest. Choice of reference book depends on person to person, find the book that best suits you the best depending on how well you are clear with the concepts and the difficulty of the questions you can handle. Taking too much time for advanced questions will be harmful to crack the exam. Finally, students need to practice as many questions as they can to get a hold of the concepts and find solutions fast. Practice will always help a candidate to crack the exam. Spending too much time on a Coordinate Geometry question might be risky and can affect the other portions of the examination. So, it is suggested to move on quickly to the next problem. 

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