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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