Question

Which algebraic representation of a transformation on a coordinate grid does NOT preserve congruence?

a) (x, y) → (x + 6, 7y + 6)
b) (x, y) + (-x, y)
c) (x, y) → (6x, 6y)
d) (x, y) + (-y, x)

Answer 1

The algebraic representation that does not preserve congruence is (x, y) + (-y, x).

Step-by-step explanation:

The algebraic representation of a transformation on a coordinate grid that does NOT preserve congruence is option d) (x, y) + (-y, x).

To determine if a transformation preserves congruence, we need to check if the pre-image and the image have the same shape and size. The transformation given in option d) involves swapping the x and y coordinates of a point. This results in a rotation of the point by 90 degrees counterclockwise or clockwise.

For example, if we use the point (1, 0) as the pre-image, the transformation (1, 0) + (-0, 1) would result in the image (1, 1). This is not congruent to the pre-image, as the shapes are different.