The point $(4,1)$ undergoes the following transformations successively:
(i) Reflection about the line $y=x$
(ii) Translation through a distance $2$ units along the positive $x$-axis
(iii) Rotation by an angle $\frac{\pi}{4}$ anticlockwise about the origin
The final position of the point is:
🎥 Video solution / Text Solution of this question is given below:
Solution:
Step 1: Reflect (4,1) about y=x → (1,4)
Step 2: Translate 2 units in +x direction → (1+2, 4) = (3,4)
Step 3: Rotate (3,4) by π/4 anticlockwise:
New x = (3 - 4)/√2 = -1/√2
New y = (3 + 4)/√2 = 7/√2
Final point = $\left(\frac{-1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$