CAT 2020 Question Paper | Quants Slot 3

CAT Previous Year Paper | CAT Quants Questions | Question 5

Have you ever tried to find the location of a fly sitting on your wall? Rene Descartes, the person who gave birth to the concept of co-ordinate geometry, did once. Try this problem from co-ordinate geometry which appeared in CAT 2020 question paper. It might help you to connect the dots properly! To find more fun questions from CAT Geometry head out here CAT Question Paper . You can expect a maximum of one question from this topic. Coordinate Geometry is a beautiful idea to learn. In this question, we have to find the area enclosed by the given equations. If you can draw the graph properly for this question then you're through.

Question 5 : 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

  1. 12
  2. 8
  3. 6
  4. 10

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Explanatory Answer

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)
Refer to the image below...
Graphs showing translations of mod of x
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.
The corresponding image to these graphs look like...
Graphing of the given equations
Now the enclosed area is the sum of areas of the rectangle and the triangle.
Enclosed Area = 2 × 4 + \\frac{1}{2}) × 2 × 2 = 8 + 2 = 10


The question is "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"

Hence, the answer is, "10"

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