﻿ The point (4, 1) undergoes the following transformation successively. (i) Reflection about the line y = x (ii) Translation through a distance 2 units along the positive direction of x-axis. (iii) Rotation through an anlge π/4 about the origin in the anticlockwise direction   (iv) Reflection about x = 0 The final position of the given point is   : Kaysons Education

# The Point (4, 1) Undergoes The Following Transformation Successively. (i) Reflection About The Line y = x (ii) Translation Through A Distance 2 Units Along The Positive direction Of x-axis. (iii) Rotation Through An Anlge π/4 About The Origin In The anticlockwise Direction   (iv) Reflection About x = 0 The Final Position Of The Given Point Is

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## Question

### Solution

Correct option is

Let BCDE be the positions of the given point A(4, 1) after the transformations (i), (ii), (iii), and (iv) successively (Fig).

 The coordinates of B are (1, 4) and that of C are (1 + 2, 4 + 0) i.e. (3, 4). Now if OC makes an angle θ with x-axis, OD make and an angle θ + π/4 with x-axis. If (h, k) denote the coordinates of D. then            h = OD cos (θ + 45o), k = sin (θ + 45o) and OD = OC = 5, sin θ = 4/5, cos θ = 3/5                     Coordinates of D are  and its reflection about x = 0 in

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