Browse Questions

# Choose the correct answer from the given four options. The point (4, 1) undergoes the following two successive transformations :  (i) Reflection about the line $y=x$  (ii) Translation through a distance 2 units along the positive x-axis  Then the final coordinates of the point are

$\begin {array} {1 1} (A)\;(4,3) & \quad (B)\;(3,4) \\ (C)\;(1,4) & \quad (D)\;\bigg( \large\frac{7}{2},\large\frac{7}{2}\bigg) \end {array}$

Toolbox:
• When a line undergoes reflection along the line $y=x$, then the coordinates also change as $(y_1,x_1)$
Step 1 :
The given line undergoes two transformation (i) $y = x$
Hence the coordinates are (1,4)
(ii) Translation through a distance 2 units along the positive $x$ - axis.
$\therefore$ The final coordinates of the point are $(1+2, 4)$
$= (3, 4)$
Hence 'B' is the correct option.