Parallelogram rstu is constructed with line ab drawn through its center. if the parallelogram is dilated using a scale factor of 4 and a line is drawn through the center of the new dilated figure, what relationship will the new line have with line ab? explain your reasoning using complete sentences.

Answer with explanation:

→Original Parallelogram called Preimage =║gm R STU

→Now, a line AB is drawn passing through the center either along the length or Breadth.

Either ,AB=R S=TU

or , AB=ST=RU

→Scale Factor of Dilation = 4 units

→So,the new ║gm that is Image has side length 4 times the length and Breadth of sides of Parallelogram R STU.

⇒Suppose the new Parallelogram Formed is ║gm J K L M.

→J K=L M=4 RS =4 TU

→KL=M J=4 ST=4 U R

→Now, the line AB is transformed into MN which will be equal to

 MN=4 AB

→So,New Line =4 ×Length of AB

Option C. Manuel's argument is correct; Paul used the incorrect formula to find the volume of square pyramid X.

Step-by-step explanation:

step 1

Find the volume of Cone W

The volume of the cone is equal to

where

B is the area of the circular base

h is the height of the cone

Find the area of the base B

we have

substitute

Find the volume

step 2

Find the volume of the square pyramid

The volume of the square pyramid is

where

B is the area of the square base

h is the height of the pyramid

we have

> is the same that the cone W

> is the same that the cone W

so

substitute

therefore

Manuel's argument is correct; Paul used the incorrect formula to find the volume of square pyramid X.