A fish was plotted on a coordinate plane. Identify the coordinates of the image of Y(-9, -1) that would create a 270-degree clockwise rotation about the origin.

Answer 1

To rotate a point on the coordinate plane, we can use a standard rotation formula. Specifically, a 270-degree clockwise rotation can be represented by the equivalent of a 90-degree counterclockwise rotation.

The coordinates \((x, y)\) after a 90-degree counterclockwise rotation about the origin can be transformed using the following formula:

\[ (x, y) \rightarrow (-y, x) \]

Given the point Y(-9, -1), we can apply this transformation:

1. Substitute \(y\) with -1 and \(x\) with -9: \[ (-1, -9) \]

So, the new coordinates after a 270-degree clockwise rotation of the point Y(-9, -1) will be:

\[ Y'(-1, -9) \]

Thus, the coordinates of the image of Y after a 270-degree clockwise rotation about the origin are \((-1, -9)\).

Answer 2

I don't think that's right

Answer 3

Let's carefully go through the steps for a 270-degree clockwise rotation about the origin again.

To rotate a point \((x, y)\) by 270 degrees clockwise, we can also think of it as rotating the point by 90 degrees counterclockwise. The transformation for a 90 degrees counterclockwise rotation is given by:

\[ (x, y) \rightarrow (-y, x) \]

So for a 270-degree clockwise rotation, the formula will be the following:

\[ (x, y) \rightarrow (y, -x) \]

Given your point \(Y(-9, -1)\):

1. Identify \(x = -9\) and \(y = -1\).
2. Substitute into the formula for a 270-degree clockwise rotation:

\[ (x, y) \rightarrow (y, -x) \rightarrow (-1, 9) \]

Thus, the coordinates after a 270-degree clockwise rotation of the point \(Y(-9, -1)\) are:

\[ Y'(-1, 9) \]

Thank you for your patience, and I appreciate your understanding. The correct coordinates for the image of Y after the rotation are \((-1, 9)\).