CAT Practice : Coordinate Geometry

For a given equation, how do we construct and visualize the graph? We tackle this important idea here.

Area under curve

    Q.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

 

  • Correct Answer
    Choice B. 2.5 sq units

Explanatory Answer

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Detailed Solution

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 = × height × sum of the parallel sides = × 1 × (3 + 2) = sq units.
Answer choice (B)

Correct Answer: 2.5 sq units



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More questions from Coordinate Geometry

  1. Straightline Shortest distance
  2. Coordinate Geometry and Probability
  3. Cogeo and greatest integer function
  4. Angle bisector theorem
  5. Area under curve
  6. Area of segment
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.