In a rigid transformation, the shape of the image remains the same as the preimage
The correct options are;
Rotation; a → b
Translation: a → d
Reflection over a horizontal line: c → e
Reflection over a vertical line: g → f
Rotation then reflection: a → h
Rotation then translation: e → j
The reasons why the above selections are correct are as follows;
Rotation; Figure <em>a</em> is rotated about a common center to figure <em>b</em> to move from <em>a</em> to <em>b</em>
Translation: Figure <em>a</em> can be translated towards the left and then upwards to reach figure <em>b</em>
Reflection over a horizontal line: A reflection over a horizontal line is similar to a reflection across the x-axis, therefore an example of a reflection over horizontal line is c → e
Reflection over a vertical line: A reflection over a vertical line will turn a left pointing triangle to a right pointing triangle as shown in g → e
Rotation then reflection: The preimage is first rotated about an axis before it is then reflected as seen in the clockwise rotation figure <em>a</em> about its axis, followed by a reflection across a vertical axis to figure <em>h</em>
Rotation then translation: The rotation and translation composite transformation can be seen in figure <em>e </em>which is rotated to point left, and then translated into the position of figure <em>j</em>
