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 3, negative 4, B prime at 5, negative 2, C prime at 5, 1, D prime at 3, negative 1.
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. (4 points)
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 7 units to the right and 8 units down. This moves A to (3, -4), B to (5, -2), C to (5, 1), and D to (3, -1).
2. Reflection: The figure is reflected across the x-axis. This changes the y-coordinates of each point to their opposites. A' becomes (3, 4), B' becomes (5, 2), C' becomes (5, -1), and D' becomes (3, 1).
Part B:
The two figures are congruent. Congruent figures have the exact same shape and size, which is true for ABCD and A'B'C'D'. The transformations that were applied (translation and reflection) do not change the shape or size of the figure, they only change its position and orientation. Therefore, the figures are congruent.