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, 0, B prime at 2, negative 2, C prime at 2, negative 5, D prime at 4, negative 3.
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: Move the figure 8 units to the right and 4 units down.
The new coordinates of ABCD after the translation are:
A: (4, 0)
B: (6, -2)
C: (6, -5)
D: (4, -3)
2. Reflection: Reflect the figure over the y-axis.
The new coordinates of ABCD after the reflection are:
A: (-4, 0)
B: (-6, -2)
C: (-6, -5)
D: (-4, -3)
3. Rotation: Rotate the figure 180 degrees counterclockwise about the origin.
The new coordinates of ABCD after the rotation are:
A: (4, 0)
B: (2, -2)
C: (2, -5)
D: (4, -3)
Part B:
The two figures are congruent. This can be seen by comparing the corresponding sides and angles of the two figures after the transformations. The side lengths remain the same and the angles are all equal. Therefore, the figures are congruent.