Verified Solution • 2025–26 Session moderate

QJEEM21Ma8fed: JEE Main 2021 Mathematics - Class 11 JEEM21Ma8fed Solution: The point P (a, b) undergoes the following three…

The point P (a, b) undergoes the following three transformations successively :

(a) reflection about the line y = x.

(b) translation through 2 units along the positive direction of x-axis.

(c) rotation through angle π4 about the origin in the anti-clockwise direction.

If the co-ordinates of the final position of the point P are (−12,72), then the value of 2a + b is equal to :

Multiple Choice Options

  • A 13
  • B 9
  • C 5
  • D 7

Step-by-Step Verified Solution

Image of A(a, b) along y = x is B(b, a). Translating it 2 units it becomes C(b + 2, a).

Now, applying rotation theorem

−12+72i=((b+2)+ai)(cos⁡π4+isin⁡π4)

−12+72i=(b+22−a2)+i(b+22+a2)

⇒ b − a + 2 = −1 ......(i)

and b + 2 + a = 7 ...... (ii)

⇒ a = 4; b = 1

⇒ 2a + b = 9

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring