# CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

###### CAT Questions | CAT Coordinate Geometry | Area under curve CAT Questions

The question is from CAT Coordinate Geometry. This is about area under curve. We need to find out the area of the region which is enclosed by given lines. Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope. It is important to cover ideas from Coordinate Geometry in your CAT Preparation

Question 5: What is the area enclosed in the region defined by y = |x – 1| + 2, line x = 1, X–axis and Y–axis?

1. 5 sq units
2. 2.5 sq units
3. 10 sq units
4. 7 sq units

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##### Method of solving this CAT Question from CAT Coordinate Geometry: For a given equation, how do we construct and visualize the graph? We tackle this important idea here.

Let us first draw y = |x|.

Now, y = |x – 1| is just a shift of ‘1’ unit to the right along the x–axis.

Now, y = |x – 1| + 2 is a shift of ‘2’ units to the top along the y–axis.

Now, let us complete the diagram by drawing the line x = 1 also.

The required area is essentially the area of the shaded region.
The point of intersection of y = |x – 1| + 2 where the y–axis can be found by substituting x = 0 in the equation.
Thus we get y = 3.

Required area = Area of the trapezium formed by the points (0, 0), (1, 0), (1, 2) and (0, 3).
Area of a trapezium = $$frac{1}{2}\\$ * height * sum of the parallel sides = $\frac{1}{2}\\$ * 1 *$3 + 2) = $$frac{5}{2}\\$ sq units. The question is "What is the area enclosed in the region defined by y = |x – 1| + 2, line x = 1, X–axis and Y–axis?" ##### Hence, the answer is 2.5 sq units Choice B is the correct answer. ###### Nail CAT 2020 with 2IIM. Live Online Course with 100+ Live Sessions 5,000 Off! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 30,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 5000/- Attend a Demo Class ## CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube #### Other useful sources for Geometry Questions | Coordinate Geometry Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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