Question

T (5, -1) is rotated 180 degrees, what is T'

Answer 1

C(2, -5) is rotated -90 degrees clockwise. find C'

Answer 2

wrong

Answer 3

To rotate a point 180 degrees around the origin, you can simply change the signs of both the x-coordinate and the y-coordinate of the point.

For the point \( T(5, -1) \):

1. Change the sign of the x-coordinate: \( 5 \) becomes \( -5 \).
2. Change the sign of the y-coordinate: \( -1 \) becomes \( 1 \).

Thus, the coordinates of the rotated point \( T' \) will be:

\[
T'(-5, 1)
\]

So, \( T' \) is \( (-5, 1) \).

Answer 4

To rotate a point \((x, y)\) by \(-90\) degrees (which is equivalent to a \(90\) degrees clockwise rotation) about the origin, you can use the following transformation:

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

For the point \( C(2, -5) \):

1. \( x = 2 \)
2. \( y = -5 \)

Using the transformation:

\[
(x, y) \rightarrow (y, -x) \implies (-5, -2)
\]

So the coordinates of the rotated point \( C' \) will be:

\[
C'(-5, -2)
\]

Thus, the final result is \( C' = (-5, -2) \).

Answer 5

I apologize for the mistake. Let’s correctly apply the transformation for a \(-90\) degrees clockwise rotation.

Given a point \( C(x, y) \), the formula to rotate it \(-90\) degrees clockwise (or equivalently, \(270\) degrees counterclockwise) around the origin is:

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

For the point \( C(2, -5) \):

1. \( x = 2 \)
2. \( y = -5 \)

Now, applying the transformation:

\[
C'(x, y) \rightarrow (y, -x) = (-5, -2)
\]

So, the rotated point \( C' \) is:

\[
C' = (-5, -2)
\]

If you were expecting a different answer, please provide specifics, and I can clarify or assist further! Thank you for your patience.