∆abc is transformed with the center of dilation at the origin. pre-image: ∆abc with vertices a(2, 5), b(6, 10), c(9, −1) image: ∆a'b'c' with vertices a' (0.5, 1.25), b' (1.5, 2.5), c' (2.25, −0.25) what is the scale factor of the dilation that maps the pre-image to the image?

1/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(2, 5) ---> A' (0.5, 1.25) =

B(6, 10) ---> B' (1.5, 2.5) =

C(9, −1) ---> C' (2.25, −0.25) =

Therefore, the scale factor of the dilation is 1/4.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.