Question

all of the other quotients choose... is ✔ is not therefore, the quotients of of the figures show that figure jklm is not a dilation of figure pqrs because all of the quotients are equivalent.

Explanation:

To determine if a figure is a dilation of another, the ratios (quotients) of corresponding side lengths must be equal (constant scale factor). If "all of the quotients are equivalent" is part of the reasoning, but the conclusion is that it's not a dilation, there's a contradiction unless the quotients are NOT all equivalent. Wait, the text here: "figure JKLM [is not] a dilation of figure PQRS because [all] of the quotients are equivalent" – no, that's incorrect. Wait, dilation requires all corresponding ratios to be equal. So if the quotients (ratios) are NOT all equivalent, then it's not a dilation. But the given text has a mix. Wait, the dropdowns: the first (after "JKLM") should be "is not" if the quotients are NOT all equivalent. Wait, the original problem's dropdowns: let's parse.

The sentence: "Therefore, the quotients of... of the figures show that figure JKLM [dropdown] a dilation of figure PQRS because [dropdown] of the quotients are equivalent."

For a dilation, all corresponding side length ratios (quotients) must be equal (same scale factor). So if "all of the quotients are equivalent" – then it WOULD be a dilation. But the checked option earlier was "is not". Wait, maybe the original problem has a typo, but based on the dropdowns:

First dropdown (after JKLM): "is not" (as checked in the image).

Second dropdown (after "because"): If it's not a dilation, the reason is that "not all" of the quotients are equivalent. But the dropdown has "all". Wait, maybe the image is showing a mistake, but following the checked options:

The answer for the first dropdown (JKLM [is not] a dilation) and the second dropdown (because [all] of the quotients... but that's contradictory. Wait, no – maybe the original problem's context (before this) had quotients that were not all equal, so the correct reasoning is: "figure JKLM is not a dilation of figure PQRS because not all of the quotients are equivalent." But the dropdown here has "all" as an option. Wait, maybe the image is from a problem where the quotients are not all equal, so the correct choices are:

First dropdown: "is not"

Second dropdown: Wait, the dropdown has "all" – maybe the problem is phrased as "because all of the quotients are NOT equivalent" – but the dropdown only has "all". Wait, perhaps the intended answer is:

Figure JKLM is not a dilation of PQRS because all of the quotients are NOT equivalent (but the dropdown has "all" – maybe the problem's wording is reversed). Given the checked option in the image for the first part is "is not", and the second dropdown has "all" selected (maybe a mistake, but following the image):

For a dilation, corresponding side length ratios (quotients) must be equal (constant scale factor). If the quotients are not all equivalent, the figure is not a dilation. The selected options in the image indicate "is not" for JKLM being a dilation, and "all" (likely a misphrasing, but following the dropdowns).

Answer:

First dropdown: is not
Second dropdown: all

(Note: There may be a wording error in the problem, as "all of the quotients are equivalent" would imply it IS a dilation. Correctly, it should be "not all" for the reason, but based on the image's dropdowns, these are the selected options.)