Question

quadrilaterals ( lmno ) and ( abcd ) are congruent. the side length of each square on the grid is 1 unit.
which of the following sequences of transformations maps ( lmno ) onto ( abcd )?
sequence a
a translation 6 units to the left and 1 unit up, then a reflection over the horizontal line through point ( a ).
sequence b
a ( 90^circ ) rotation about point ( o ), then a translation 6 units to the left and 1 unit up.
choose 1 answer:
a only sequence a
b only sequence b
c both
d neither

Explanation:

Step1: Analyze Sequence A

First, translate \( LMNO \) 6 units left and 1 unit up. This moves the figure closer to \( ABCD \)'s position. Then, reflect over the horizontal line through \( A \). Since the quadrilaterals are congruent, this reflection should map \( LMNO \) onto \( ABCD \) as the orientation and position after translation and reflection align.

Step2: Analyze Sequence B

A \( 90^\circ \) rotation about \( O \) would change the orientation of \( LMNO \) in a way that a subsequent translation (6 left, 1 up) won't align it with \( ABCD \). The rotation about \( O \) disrupts the necessary alignment, so Sequence B doesn't work.

Answer:

A. Only sequence A