If E partitions CD by a ratio of 1/8, then which of the following could be the location of E?

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If E partitions CD by a ratio of 1/8, then which of the following could be the location of E?

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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-7 -5 -3 -1
We're going to need a bit more information about CD!
ok i attach the line

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what is the length of CD?
16?
@whpalmer4 is that right ?
Let me look!
ok
yes, that appears to be correct.
are you sure that 1/8 is the ratio?
yes it is
because if it is, we won't land exactly on any of those numbers in the answer choices
did you see the picture i attached?
we have 16 units to divide into 1+8=9 parts, and then we'll take 1/9 of those parts from an endpoint to find our partition.
ok so how do i do that?
possibly the problem expects you to choose -7 as your answer, but that isn't strictly speaking correct. partition CD by 1/8 means that CE and ED have the ratio 1:8, which means we must chop CD into 9 equal parts, and place E 1 part toward D from C. CD goes from -9 to +7 in your diagram, which is a total of 16 units. 16/(8+1) = 16/9 and neither 1*16/9 nor 8*16/9 is a round number, yet all the answer choices are round numbers.
16/9 = 1.77777777... so if we add -9 + 1.777777... we get -7.22222... which is close to -7, but not the same. But all the other answers are even further removed from the 1/8 point, so that's the best of the bunch, I suppose.
ok that makes sense maybe were supposed to round
If the ratio was 1/7, then we could do the problem correctly. CD is 16 units long, divided into 1+7=8 parts gives us 2 units per part. Our ratio calls for us to go 1 part = 2 units toward D from C, so -9 + 2 = -7 and that is exactly what one of the answer is. That's what made me ask if you had copied the problem correctly (you had, but I think the problem is incorrect. It happens much more often than it should, given what textbook publishers charge!)
Anyhow, do you at least understand how I worked the problem?
yes i do thank you so much ill put -7 but ill eamil my teacher
Yes, that would be good. If they insist that the problem is correct as written, let me know and I will supply you with some problems for them that demonstrate the flaw in their understanding :-)

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