Question

The image of a point under D O, 3 is (7, 2). The preimage of the point is _____.

(21, 6)
(10, 5)
(4, -1)
(7/3, 2/3)

Answer 1

(7/3, 2/3)

Explanation:

Answer 2

The correct option is 4. The coordinates of preimage are
`((7)/(3),(2)/(3))`.

Explanation:

According to
`D_(O,3)`, the figure dilated by scale factor 3 and he center of dilation is origin.

If a the scale factor is k and center of dilation is origin, then

`P(x,y)\rightarrow P'(kx,ky)`

The scale factor is 3.

`P(x,y)\rightarrow P'(3x,3y)`

Since the coordinates of image are (7,2).

`(3x,3y)=(7,2)`

Equate both sides.

`3x=7`

`x=(7)/(3)`

`3y=2`

`y=(2)/(3)`

Therefore the coordinates of preimage are
`((7)/(3),(2)/(3))`.