2. Triangle GHI with vertices G(-1,6), H(-1,3), and I(-6, 6): a) translation along the vector (7,-5)

b) reflection in the line y = -3

a) The vertices of the triangle G'H'I' are , and , respectively.

b) The triangle G''H''I'' have vertices at , and .

Step-by-step explanation:

a) From Linear Algebra, we define the translation by the following vector:

(1)

Where:

- Original point, dimensionless.

- Translated point, dimensionless.

- Translation vector, dimensionless.

If we know that , , and , then the vertices of the triangle G'H'I' are, respectively:

(2)

(3)

(4)

The vertices of the triangle G'H'I' are , and , respectively.

b) From Linear Algebra, we define the reflection with respect to a horizontal line as follows:

(5)

Where:

- Original point, dimensionless.

- Reflection point, dimensionless.

If we know that and , then the location of point G'' is:

(6)

If we know that and , then the location of the point H'' is:

(7)

If we know that and , then the location of the point I'' is:

(8)

The triangle G''H''I'' have vertices at , and .

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.