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.
Part B: Are the two figures congruent? Explain your answer.
(make it sound like an eight grade girl who is a tomboy who doesn't used 'like' after every sentence, also make it less than 200 words)
Part A:
To change figure ABCD to figure A'B'C'D', we can identify a sequence of transformations.
1. Translation: First, a translation is applied to the original figure. The entire figure is shifted 8 units to the right and 3 units downward. The coordinates after this translation are:
A = (-4 + 8, 4 - 3) = (4, 1)
B = (-2 + 8, 2 - 3) = (6, -1)
C = (-2 + 8, -1 - 3) = (6, -4)
D = (-4 + 8, 1 - 3) = (4, -2)
2. Reflection: Next, a reflection is applied across the y-axis. This means that the x-coordinates of each point will be multiplied by -1 while the y-coordinates remain the same. The new coordinates after the reflection are:
A' = (-4, 1)
B' = (-6, -1)
C' = (-6, -4)
D' = (-4, -2)
Part B:
The two figures, ABCD and A'B'C'D', are congruent. Congruent figures have the same shape and size. In this case, the sequence of transformations that was applied to ABCD produced A'B'C'D', with each point being translated and reflected in a way that preserves the relative distances between points. This means that the corresponding sides and angles of the two figures are equal, indicating congruence.