Which reflection rule, if any, can be used to prove that rectangle A'(-8, -3), B'(-2, -3), C'(-2, -6), D'(-8, -6) are congruent?
A (x, y) → (-x, y)
B (x, y) → (x, -y)
C (x, y) → (-x, -y)
D The rectangles are not congruent.
Which reflection rule, if any, can be used to prove that rectangle A'(-8, -3), B'(-2, -3), C'(-2, -6), D'(-8, -6) are congruent
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To determine which reflection rule can be used to prove that rectangle A'(-8, -3), B'(-2, -3), C'(-2, -6), D'(-8, -6) are congruent, we should first analyze the orientation of the rectangle.
The points of rectangle A’B’C’D’ suggest that it is positioned in the fourth quadrant. To reflect this rectangle across the x-axis (rule B: (x, y) → (x, -y)), it would transform all y-coordinates to their opposites. However, this does not lead to a congruent rectangle since the corners would change but not align with the original points.
For the other options:
– Option A (x, y) → (-x, y) reflects points across the y-axis.
– Option C (x, y) → (-x, -y) reflects points across the origin.
Given that reflecting over the x-axis flips the rectangle above the x-axis, it will not yield the same vertices after reflection.
Therefore, the answer is D: The rectangles are not congruent.
The rectangles cannot be made to coincide through any of the given reflection rules. Keep up the good work, and feel free to ask more questions!