Rectangle $ABCD$ABCD is translated and then reflected to create rectangle $ABCD$A′B′C′D′ . Do rectangle $ABCD$ABCD and rectangle $ABCD$A′B′C′D′ have the same area? Justify your answer.

Question

Rectangle $ABCD$ABCD​ is translated and then reflected to create rectangle $ABCD$A′B′C′D′​ . Do rectangle $ABCD$ABCD​ and rectangle $ABCD$A′B′C′D′​ have the same area? Justify your answer.

jlo2niT · Accepted Answer

When we translate the rectangle ABCD we do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the figure does not change. When applying the transformations we will transform each point and then redraw the figure.  when we reflect the rectangle we are just shifting the rectangle to the other side of either x or y axis (according to the reflection) at a distance equidistant from the axis. Hence each vertex shifts to a new position but remains at the same distance from the other vertex as previously before the reflection.  Hence there would be no change in the area of the rectangle if we translate and then reflect it.

Rectangle $ABCD$ABCD is translated and then reflected to create rectangle $A'B'C'D'$A′B′C′D′ . Do rectangle $ABCD$ABCD and rectangle $A'B'C'D'$A′B′C′D′ have the same area? Justify your answer.

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