Question

Consider that Δxyz is reflected across the y-axis and translated 2 units down. Choose all true statements about the transformation.

1) The x-coordinate of each point is negated.
2) The y-coordinate of each point is negated.
3) The z-coordinate of each point is negated.
4) Each point is moved 2 units down in the y-direction.

Answer 1

When ∆xyz is reflected across the y-axis, the x-coordinate is negated, and when it is translated 2 units down, the y-coordinate decreases by 2; the z-coordinate is unaffected in the context of the problem.

Step-by-step explanation:

When ∆xyz is reflected across the y-axis, the x-coordinate of each point is negated (flipped in the horizontal direction), while the y-coordinate and z-coordinate remain unchanged if it is a three-dimensional space. Next, translating the figure 2 units down affects only the y-coordinate, subtracting 2 from each point's y-coordinate. The z-coordinate does not change due to a translation in the xy-plane. As for the options given:

1. The x-coordinate of each point is negated. True, this is what happens in a reflection across the y-axis.
2. The y-coordinate of each point is negated. False, reflecting across the y-axis does not affect the y-coordinate.
3. The z-coordinate of each point is negated. False, the initial comment on the z-coordinate change only applies to 3D transformations and the question does not specify a three-dimensional reflection.
4. Each point is moved 2 units down in the y-direction. True, this is what happens in the translation.