Answer:
The pair of the rectangles with dimensions 2 , 3 and 3 , 4 proved that Carly's statement is incorrect
Step-by-step explanation:
* Lets explain how to solve the problem
- Dilation is a type of transformation that enlarges or reduces a figure
- To find the image of any figure after dilation by scale factor k we
multiply all the dimensions of the figure by k
- The scalar factor measures how much larger or smaller the image is
* Lets solve the problem
- In the first figure:
- There are two rectangles the dimensions of the small one are 2 , 4
and the corresponding dimensions of the large one are 4 , 8
∵ 4/2 = 2 and 8/4 = 2
∴ The scale factor is 2
∴ The corresponding sides are proportion
∴ The pair of rectangles are dilation
- In the second figure:
- There are two rectangles the dimensions of the small one are 2 , 4
and the corresponding dimensions of the large one are 3 , 6
∵ 3/2 = 1.5 and 6/4 = 1.5
∴ The scale factor is 1.5
∴ The corresponding sides are proportion
∴ The pair of rectangles are dilation
- In the third figure:
- There are two rectangles the dimensions of the small one are 2 , 3
and the corresponding dimensions of the large one are 3 , 4
∵ 2/3 = 0.67 and 3/4 = 0.75
∵ 2/3 ≠ 3/4
- The dimensions are NOT proportion
∴ The pair of rectangles are not dilation
- In the fourth figure:
- There are two rectangles the dimensions of the small one are 1.5 , 2
and the corresponding dimensions of the large one are 3 , 4
∵ 1.5/3 = 0.5 and 2/4 = 0.5
∴ The scale factor is 0.5
∴ The corresponding sides are proportion
∴ The pair of rectangles are dilation
* The pair of the rectangles with dimensions 2 , 3 and 3 , 4 proved
that Carly's statement is incorrect
# Look to the attached figure
