Question

Point A (-7,-2) is rotated 270° counterclockwise and then shifted down 3 units. What are to coordinates of K’ ?

A. (2,4)
B. (-2, -7)
C. (-2, 4)
D. (7, -5)

Answer 1

The new position of point A after a 270° counterclockwise rotation and shifting down by 3 units is (2, 4), making option A the correct answer.

Step-by-step explanation:

The student's question involves finding the new position of point A after a rotation by 270° counterclockwise followed by a translation (shifting down by 3 units). These kinds of transformations are common in coordinate geometry, a typical topic in high school mathematics.

To find the coordinates of the transformed point, also known as K', we can follow two steps:

1. Rotate point A (-7, -2) by 270° counterclockwise. After this rotation, the new coordinates can be found by switching the x and y values and then changing the sign of the new x-coordinate. As a result, the rotated point A will have coordinates (2, 7).
2. Shift the rotated point down by 3 units which means subtracting 3 from the y-coordinate. This gives us the new point K' with coordinates (2, 4).

Therefore, the correct answer is A. (2,4).