Question

Identify the rotation function mapping used to turn A (-7,4) to A' (-4,-7).
A. (x,y) → (2x, 2y)
B. (x,y) → (-у, х)
C. (x,y) (x, -у)
D. (x,y) (y, х)

Answer 1

To find the rotation function that maps point A (-7, 4) to A' (-4, -7), we can analyze the transformation of the coordinates through each given option.

1. **Original Point** A = (-7, 4)
2. **Transformed Point** A' = (-4, -7)

Let's examine the options:

**A. (x,y) → (2x, 2y)**
This multiplies both coordinates by 2.
For A (-7, 4):
(2*(-7), 2*4) = (-14, 8) which does not match A'.

**B. (x,y) → (-y, x)**
This switches and negates the x-coordinate with the y-coordinate.
For A (-7, 4):
(-4, -7) which matches A'.

**C. (x,y) → (x, -y)**
This negates the y-coordinate.
For A (-7, 4):
(-7, -4) which does not match A'.

**D. (x,y) → (y, x)**
This switches the x and y coordinates.
For A (-7, 4):
(4, -7) which does not match A'.

The option B transformation, which is (x,y) → (-y, x), successfully maps point A (-7, 4) to point A' (-4, -7).

Therefore, the correct answer is **B. (x,y) → (-y, x)**.