Question

The image of (6, 9) under a dilation is (4, 6).

Answer 1

For this case we have the following ordered pairs:
 (6, 9)
 (4, 6)
 The scale factor can be found in two different ways:
 $k = 6/4 = 3/2 = 1.5 k = 9/6 = 3/2 = 1.5$
 Therefore, the scale factor is given by:
 $k = 1.5$
 Answer:
 The scale factor of the dilation is 1.5

Answer 2

Answer:

2/3.

Step-by-step explanation:

The exercise says us that we multiply (6,9) by a factor (in the enunciated is called a dilation) and obtain (4,6). That is

(6,9)x=(6x,9x) = (4,6). (in the exercise the x is represented with a0)

Now, one ordered pair is equal to another if both first components are equal and also if both second components are equal. Then,

6x = 4 and 9x=6

x = 4/6 and x = 6/9

x = 2/3 and x= 2/3.

So, the scale factor of the dilation is 2/3.