Question

This image shows a geometric design on a coordinate plane, with several labeled points connected by orange lines. Here's the breakdown:

Labeled Points:

S: (-12, 2)

H: (-11, 0)

I: (-9, 2)

F: (-6, 0)

Y: (-9, -1)

Pattern: These points form a distinct shape. The labels (S, H, I, F, Y) are in blue, and the connecting lines are orange.

Axes Range: The x-axis spans from -15 to 5, and the y-axis from -5 to 10.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′(−9,1)
upper Y prime left parenthesis negative 9 comma 1 right parenthesis

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

Y′(1,−9)

Answer 1

To find the coordinates of point Y (-9, -1) after a 270-degree clockwise rotation about the origin, we can use the following transformation rule:

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

Applying this transformation to point Y (-9, -1):

1. Original coordinates: \(x = -9\), \(y = -1\)
2. Apply the transformation:
- The new x-coordinate is \(y = -1\)
- The new y-coordinate is \(-x = -(-9) = 9\)

Thus, the coordinates after the rotation are:
\[
Y'(-1, 9)
\]

This matches the option:
**Y′(−1,9)**.

So the correct answer is:
**Y′(−1, 9)**.