Question

Question

Use the image to answer the question.

Five solid lines join five plotted points labeled upper I, upper F, upper Y, upper H, and upper S on a coordinate plane. An unlabeled point is also plotted on the plane.

A fish was plotted on a coordinate plane. Identify the coordinates of the image of Y
that would create a 270-degree clockwise rotation about the origin.

(1 point)
Responses

Y′(1,9)
upper Y prime left parenthesis 1 comma 9 right parenthesis

Y′(1,−9)
upper Y prime left parenthesis 1 comma negative 9 right parenthesis

Y′(−1,9)
upper Y prime left parenthesis negative 1 comma 9 right parenthesis

Y′(−9,1)

Answer 1

To find the coordinates of point Y after a 270-degree clockwise rotation about the origin, we can use the rotation rules for the coordinate plane.

For a 270-degree clockwise rotation, the transformation of a point (x, y) is given by:

\[ (x', y') = (y, -x) \]

Let's denote the coordinates of point Y as (x, y).

1. Suppose the coordinates of Y are (a, b).
2. After a 270-degree clockwise rotation, the new coordinates \( Y' \) would be \( (b, -a) \).

From the choices given, we need to identify which of the points corresponds to a 270-degree rotation of point Y.

• If we take the first option, Y′(1, 9), it implies that Y was at the coordinates (9, -1), which does not correspond to any common transformations.
• The second option, Y′(1, −9), implies Y was at the coordinates (−9, −1) with an incorrect transformation.
• The third option, Y′(−1, 9), implies Y was at (9, 1), which follows the transformation of (y, -x).
• Lastly, Y′(−9, 1) suggests Y was at (1, -9), also incorrect.

Assuming we do not know the coordinates of point Y explicitly but want the transformation of the point Y, one would need the original coordinates of Y to determine the correct location after a 270-degree clockwise rotation.

If the original coordinates of Y were known beforehand from the context or if they were clearly defined, you would apply the transformation to select the correct response given above.

Without that data, I can only conclude that:

• The correct choice based on transformation clarification indicating a 270-degree clockwise rotation is that \( Y' \) would be \( (b, -a) \).

However, since we do not have the (x, y) coordinate of Y to input at the beginning, it’s a matter of identifying whether we assume common coordinates here from context or visual in a graph, which changes the effectiveness of responses. So, unless given the specifics in coordinates beforehand for Y, accurately choosing a response is impossible.

If the question provides Y's coordinates, you'd apply them to determine which response is correct from what we discussed above.