Question

When the transformation (x,y) → (x – 2,y - 5) is performed on point R, its image is point R' (10,7). What are the coordinates of R?

A) (8.2)
B (-8,-2)
C) (12,-12)
D) (12, 12)​

Answer 1

The original coordinates of point R before the transformation (x, y) → (x - 2, y - 5) are (12, 12), obtained by reversing the transformation applied to R' (10,7).

Step-by-step explanation:

The student's question asks about finding the original coordinates of a point before a given transformation has been applied. In this case, the transformation applied is (x, y) → (x - 2, y - 5), and the transformed point, R', is given as (10,7). To obtain the coordinates of the original point, R, we reverse the transformation by adding 2 to the x-coordinate and 5 to the y-coordinate of the transformed point. Therefore, the coordinates of R are (12, 12).

Step-by-step explanation:

1. Identify the transformation that has been applied to the original point R, which is subtracting 2 from the x-coordinate and 5 from the y-coordinate.
2. Since the image, R', after the transformation is given as (10,7), apply the inverse transformation to find R, which means adding 2 to the x-coordinate and 5 to the y-coordinate.
3. By adding 2 to the x-coordinate (10 + 2) we get 12, and by adding 5 to the y-coordinate (7 + 5) we get 12, which gives us the original coordinates of R as (12, 12).