Question

The point Q(−5,−9) is rotated −270° about the origin. Select the location of Q′ .

A. Q'(9,5)
B. Q' (-5,9)
C. Q' (5,9)
D. Q' (9,-5)

Answer 1

Are you sure you are correct.

Answer 2

To find the new coordinates of point Q(-5, -9) after a rotation of -270° about the origin, we can first convert the angle to a positive angle.

-270° is equivalent to +90° since rotating clockwise is negative and counter-clockwise is positive.

To rotate a point (x, y) by 90° counter-clockwise about the origin, the new coordinates (x', y') are given by:
- \( x' = -y \)
- \( y' = x \)

Now, applying these transformations to the point Q(-5, -9):

1. \( x' = -(-9) = 9 \)
2. \( y' = -5 \)

Thus, the new coordinates after rotating Q(-5, -9) -270° (or +90°) about the origin are Q'(9, -5).

Therefore, the correct answer is:
**D. Q' (9, -5)**

Answer 3

Let's go through the rotation of point \( Q(-5, -9) \) about the origin by an angle of \(-270^\circ\) step by step to ensure accuracy:

1. **Understanding the rotation**:
- A rotation of \(-270^\circ\) is equivalent to rotating by \(90^\circ\) counterclockwise, since \(-270 + 360 = 90\).

2. **Rotation transformation**:
- The rules for rotating a point \((x, y)\) by \(90^\circ\) counterclockwise around the origin are:
- \( x' = -y \)
- \( y' = x \)

3. **Substituting in the original point**:
- For point \( Q(-5, -9) \):
- \( x = -5 \)
- \( y = -9 \)

4. **Calculating the new coordinates**:
- \( x' = -y = -(-9) = 9 \)
- \( y' = x = -5 \)

So, the coordinates of \( Q' \) after the rotation are:
- \( Q'(9, -5) \)

Therefore, the correct answer is:
**D. \( Q'(9, -5) \)**

Thank you for your patience, and I confirm that my previous response was accurate.