Question

Mallory is investigating transformations in the coordinate plane. She makes the claims shown in the options below.

Select each claim that is true for all points in the coordinate plane.
A A translation of 4 units down takes the point (x, y) to (x, y - 4).
B A reflection over the line y = -x takes the point (x, y) to (x, y).
C A reflection over the y-axis takes the point (x,y) to (-x, y).
D A rotation of 180° clockwise about the origin takes the point (x, y) to (v. -X).

Answer 1

True claims about transformations in the coordinate plane are that a translation of 4 units down takes the point (x, y) to (x, y - 4), and a reflection over the y-axis takes the point (x, y) to (-x, y).

Step-by-step explanation:

Mallory is investigating transformations in the coordinate plane and is evaluating the truthfulness of several claims about how points in the plane are affected by these transformations.

• Claim A: True. A translation of 4 units down changes the y-coordinate by subtracting 4, hence (x, y) becomes (x, y - 4), moving the point vertically downward in the coordinate system.
• Claim B: False. A reflection over the line y = -x takes the point (x, y) to (-y, -x), not (x, y). This reflection causes a swap and negates the coordinates.
• Claim C: True. A reflection over the y-axis changes the sign of the x-coordinate, hence (x, y) becomes (-x, y).
• Claim D: False. A 180° clockwise rotation about the origin takes the point (x, y) to (-x, -y), not (v. -X).

Thus, the true claims about transformations for all points in the coordinate plane are Claim A and Claim C.