A rectangle has vertices E(-4, 8), F(2, 8), G(2, -2) and H(-4, -2). The rectangle is dilated with the origin as the center of dilation so that G' is located at (5, -5). Which algebraic representation represents this dilation?

The dilation on any point of the rectangle is .

Step-by-step explanation:

From Linear Algebra, we define the dilation of a point by means of the following definition:

(1)

Where:

- Coordinates of the point G, dimensionless.

- Center of dilation, dimensionless.

- Scale factor, dimensionless.

- Coordinates of the point G', dimensionless.

If we know that , and , then scale factor is:

The dilation on any point of the rectangle is:

(2)

The dilation on any point of the rectangle is .

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional