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 π 4 about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point P are - 1 2 , 7 2 , then the value of 2 a + b is equal to:

Question

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 π 4 about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point P are - 1 2 , 7 2 , then the value of 2 a + b is equal to:, 13, 9, 5, 7

MARKS App · Accepted Answer

Image of A a , b along y = x is P ' b , a . Translating it 2 units along positive direction of x - axis it becomes P " b + 2 , a . Now, applying Rotation theorem - 1 2 + 7 2 i = b + 2 + a i cos π 4 + i sin π 4 Multiplying the complex numbers we get, - 1 2 + 7 2 i = b + 2 2 - a 2 + i b + 2 2 + a 2 ⇒ b - a + 2 = - 1 . . . 1 and b + 2 + a = 7 . . . 2 ⇒ a = 4 ; b = 1 ⇒ 2 a + b = 9

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