Figure ABCD is transformed to obtain figure A′B′C′D′:
A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 1, B prime at 2, negative 1, C prime at 2, negative 4, D prime at 4, negative 2.
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer.
Part A: The sequence of transformations that changes figure ABCD to figure A'B'C'D' is as follows:
1. Translation: The figure is translated 8 units to the right and 3 units down. This can be seen by comparing the coordinates of point A and point A' (negative 4, 4 to 4, 1). The new coordinates of the other points are B' (2, -1), C' (2, -4), and D' (4, -2).
2. Reflection: The figure is reflected across the y-axis. This can be seen by comparing the x-coordinates of the original points and the new points. The x-coordinates of the original points are all negative, while the x-coordinates of the new points are all positive.
Therefore, the sequence of transformations is a translation followed by a reflection.
Part B: The two figures are congruent.
Two figures are congruent if they have the same size and shape. Since the sequence of transformations from figure ABCD to figure A'B'C'D' only involves a translation and a reflection, which preserve size and shape, the two figures are congruent.