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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

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

1 Answer

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.
answered Jul 6, 2014 by thanvigandhi_1
 

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