Question
The point Q(-5,-9) is rotated -270 degrees about the origin. Select the location of Q'.
(9,-5)
(9,-5)
(9,5)
(9,5)
(-5, 9)
(-5, 9)
(5,9)
choose which ever one is the best
(9,-5)
(9,-5)
(9,5)
(9,5)
(-5, 9)
(-5, 9)
(5,9)
choose which ever one is the best
Answers
GPT-4o mini
To rotate the point Q(-5, -9) by -270 degrees about the origin, you can use the following rule for rotation:
- A rotation of -270 degrees is equivalent to a rotation of +90 degrees (since rotating clockwise is negative and rotating counterclockwise is positive).
The coordinates of a point \((x, y)\) rotated by 90 degrees counterclockwise are transformed to \((-y, x)\).
Let's apply this transformation to the point Q(-5, -9):
1. Identify the coordinates: \(x = -5\) and \(y = -9\).
2. Apply the rotation formula:
- New x-coordinate: \(-y = -(-9) = 9\)
- New y-coordinate: \(x = -5\)
So, Q' will be at the coordinates \((9, -5)\).
From the options given:
- (9, -5) is not listed.
- However, (9, 5) appears, but it's incorrect since the correct point after rotation is (9, -5) and not (9, 5).
Among the choices, none are correct for the rotated point Q'.
- A rotation of -270 degrees is equivalent to a rotation of +90 degrees (since rotating clockwise is negative and rotating counterclockwise is positive).
The coordinates of a point \((x, y)\) rotated by 90 degrees counterclockwise are transformed to \((-y, x)\).
Let's apply this transformation to the point Q(-5, -9):
1. Identify the coordinates: \(x = -5\) and \(y = -9\).
2. Apply the rotation formula:
- New x-coordinate: \(-y = -(-9) = 9\)
- New y-coordinate: \(x = -5\)
So, Q' will be at the coordinates \((9, -5)\).
From the options given:
- (9, -5) is not listed.
- However, (9, 5) appears, but it's incorrect since the correct point after rotation is (9, -5) and not (9, 5).
Among the choices, none are correct for the rotated point Q'.