28. Describe the sequence of
transformations from ΔA to ΔB.
B. reflection over
the x-axis and
translation a
2 units down.
C. 90° rotation
counterclockwise
and a translation
1 unit right.
D. reflection over
the y-axis and a
translation 2 units
down.
Explain: To show congruence a
transformation of both _________________ and _______________ must be completed because
To show congruence between ΔA and ΔB, a transformation of both shape and position must be completed.
In option B, the transformation includes a reflection over the x-axis, which would change the shape of ΔA by flipping it upside down, and a translation 2 units down, which would change the position of ΔA by moving it downwards. Both the shape and position of ΔA would be transformed to match ΔB.
In option C, the transformation includes a 90° rotation counterclockwise, which would change the shape of ΔA by rotating it, and a translation 1 unit right, which would change the position of ΔA by moving it to the right. Both the shape and position of ΔA would be transformed to match ΔB.
In option D, the transformation includes a reflection over the y-axis, which would change the shape of ΔA by flipping it horizontally, and a translation 2 units down, which would change the position of ΔA by moving it downwards. Both the shape and position of ΔA would be transformed to match ΔB.
Overall, to show congruence between ΔA and ΔB, both shape-changing and position-changing transformations must be completed.
its d but explain why
Option D involves a reflection over the y-axis, followed by a translation 2 units down.
The reflection over the y-axis would change the shape of ΔA by flipping it horizontally. This means that any points on ΔA that were originally on the right side of the y-axis would now be on the left side, and vice versa.
The translation 2 units down would change the position of ΔA by moving it downwards. Each point on ΔA would be shifted vertically by 2 units downward.
By performing both the reflection and translation, both the shape and position of ΔA would be transformed to match ΔB. The reflection over the y-axis would ensure that the orientation of the shape matches, while the translation 2 units down would ensure that the positions of the points match.