Question

What are the coordinates of the image of R for a dilation with center (0,0) and a scale factor of 1/3

A) (1, -2/3)
B) (9, -6)
C) (2, -1/3) (1, 4/3)

Answer 1

Answer: The correct option is (A)
`\left(1,-(2)/(3)\right).`

Step-by-step explanation: We are given to find the co-ordinates of the image of the point R for a dilation with center (0, 0) and a scale factor of
`(1)/(3).`

We can see from the given figure that

the co-ordinates of the point R are (3, -2).

Since the figure PQR is dilated with center of dilation as origin (0, 0), so the co-ordinates of the image of point R will be one-third of the co-ordinates of the point R.

Therefore, the co-ordinates of the image of R are

`(1)/(3)* (3, -2)\\\\=\left((3)/(3),-(2)/(3)\right)\\\\\\=\left(1,-(2)/(3)\right).`

Thus, the co-ordinates of the image of point R are
`\left(1,-(2)/(3)\right).`.

Option (A) is CORRECT.