Question

Draw a square whose vertices are (2,2), (4,2), (4,4) and (2,4). Reflect the square in the y-axis and then reflect the image in the origin. What single transformation would give the same result?

Answer 1

The given points are (2,2), (4,2), (4,4) and (2,4).

$M_y\to$ (-2,2), (-4,2), (-4,4) and (-2,4)
$\because$ (When a point is reflected in the $y-axis$ the sign of the abscissa changes).

$M_O\to$ (2,-2),(4,-2), (4,-4) and (2,-4).........(i)
$\because$ (When a point is reflected in the origin the sign of both the abscissa and ordinate changes).

When the points (2,2), (4,2), (4,4) and (2,4) are reflected in the $x-axis$ we get (2,-2),(4,-2), (4,-4) and (2,-4)..........(ii)
$\because$ (When a point is reflected in the $x-axis$ the sign of the ordinate changes.

Comparing (i) and (ii) we note that the required single transformation is reflection in the x-axis.