Question

preimage
image
scale factor = 4
kieran’s work
5 x 9 = 45
45 x 4 = 180
(preimage rectangle with 5 in and 9 in dimensions)
kieran says the area of the image is 180 in². do you agree? why or why not?

• i disagree. kieran made an error when calculating the area of the preimage.
• i disagree. kieran used the wrong formula when calculating the area of the preimage.
• i agree. kieran correctly found the area of the preimage and applied the scale factor twice.
• i disagree. kieran correctly found the area of the preimage but only applied the scale factor once.

Explanation:

1. First, find the area of the preimage (rectangle): length = 9 in, width = 5 in, so area \( A_{pre}=\ 9\times5 = 45\ in^{2}\).
2. When scaling a figure with a scale factor \( k \), the area of the image scales by \( k^{2}\) (since area is a two - dimensional measurement). Here, the scale factor \( k = 4\), so the area of the image should be \( A_{image}=A_{pre}\times k^{2}=45\times4^{2}=45\times16 = 720\ in^{2}\).
3. Kieran calculated \( 45\times4 = 180\), which means he only applied the scale factor once (multiplied by \( k\) instead of \( k^{2}\)), so his answer of \( 640\ in^{2}\) is wrong. The correct reason for disagreeing is that he correctly found the pre - image area but only applied the scale factor once.

Answer:

I disagree. Kieran correctly found the area of the preimage but only applied the scale factor once.