Which transformations do not preserve congruence? (Choose 2)
Responses
A (x, y) → (x+2, y–1)( x , y ) → ( x +2, y– 1)
B
(x, y) → ( 1 x, 1 y)
8 8( x , y ) → ( 1 x , 1 y ) 8 8
C (x, y) → (–x, –y)( x , y ) → (– x , – y )
D (x, y) → (x, –y)( x , y ) → ( x , – y )
E (x, y) → (2.5x, 2.5y)( x , y ) → (2.5 x , 2.5 y )
F (x, y) → (y, –x)
C and F do not preserve congruence.
The transformations that do not preserve congruence are:
A) (x, y) → (x+2, y–1)
C) (x, y) → (–x, –y)
To determine which transformations do not preserve congruence, we need to understand what it means for a transformation to preserve congruence.
A transformation preserves congruence if it does not change the relative positions or distances between points. In other words, if two figures are congruent, then applying the transformation to both figures will result in two new figures that are still congruent.
Let's analyze each option to see if they preserve congruence:
A) (x, y) → (x+2, y–1)
This transformation involves shifting all points in the figure 2 units to the right and 1 unit down. Shifting a figure does not change its shape or size, so this transformation preserves congruence.
B) (x, y) → (1x, 1y)
This transformation scales all points in the figure by a factor of 1 in both the x and y directions. Scaling a figure by a factor of 1 does not change its shape or size, so this transformation preserves congruence.
C) (x, y) → (–x, –y)
This transformation reflects all points in the figure across the origin (0,0). Reflection changes the orientation of the figure but does not change its size or shape, so this transformation preserves congruence.
D) (x, y) → (x, –y)
This transformation reflects all points in the figure across the x-axis. Like the previous transformation, reflection changes the orientation but not the size or shape, so this transformation preserves congruence.
E) (x, y) → (2.5x, 2.5y)
This transformation scales all points in the figure by a factor of 2.5 in both the x and y directions. Scaling changes the size of the figure, so this transformation does not preserve congruence.
F) (x, y) → (y, –x)
This transformation swaps the x and y coordinates of all points and then reflects them across the y-axis. This transformation changes the shape and orientation of the figure, so it does not preserve congruence.
Therefore, the transformations that do not preserve congruence are E) (x, y) → (2.5x, 2.5y) and F) (x, y) → (y, –x).