10. What are the coordinates of point B in the xy-plane above ?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)
Can anybody help?
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What are the coordinates of point B in the xy-plane above ?
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DeepakR
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Since AB=BC the 2 sides are equal. Hence Length of both sides should be the same. I applied the answer choice (6, 28) as B and tried AB=sqrt(14^2+28^2) and BC=sqrt(14^2+28^2) and found that both are equal.
Ans.) B = (6, 28)
PS: You dont need to calculate the sqrt value. Just keep it and compare both.
Ans.) B = (6, 28)
PS: You dont need to calculate the sqrt value. Just keep it and compare both.
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gaggleofgirls
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The length of AC is the positive different between -8 and 20, so it is 28 long.
Since AC=BD, then it is 28 in height, so the y value is 28. The immediately narrows it down to answers B or D.
Knowing that AB=BD lets us know that point D is the midoint of AC, so point D is 214 away from either endpoint (20-14 = 6) so D is at 6,0
Therefore Point B is at 6,28.
Answer is B
-Carrie
Since AC=BD, then it is 28 in height, so the y value is 28. The immediately narrows it down to answers B or D.
Knowing that AB=BD lets us know that point D is the midoint of AC, so point D is 214 away from either endpoint (20-14 = 6) so D is at 6,0
Therefore Point B is at 6,28.
Answer is B
-Carrie
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kamu
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how???[/i]gaggleofgirls wrote:The length of AC is the positive different between -8 and 20, so it is 28 long.
Since AC=BD, then it is 28 in height, so the y value is 28. The immediately narrows it down to answers B or D.
Knowing that AB=BD lets us know that point D is the midoint of AC, so point D is 214 away from either endpoint (20-14 = 6) so D is at 6,0
Therefore Point B is at 6,28.
Answer is B
-Carrie
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gaggleofgirls
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Sorry for my typo, where it says '214' it should be 14.
Other than that, I am not sure what part is confusing. Can you clarify what part of my answer doesn't make sense?
-Carrie
Other than that, I am not sure what part is confusing. Can you clarify what part of my answer doesn't make sense?
-Carrie
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Bhattu
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Carrie, Not sure how you get AB = BD all we have in the stem is AC=BD and AB =BC. Maybe I am missing something obvious?
The way I calculated it was as follows
28, because we know AB=BD, therefore y = 28, and we know that x has to be less than -8 or 8, therefore (6, 28) is the only possible answer
The way I calculated it was as follows
28, because we know AB=BD, therefore y = 28, and we know that x has to be less than -8 or 8, therefore (6, 28) is the only possible answer
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Solution:
Since AB = BC, triangle ABC is an isosceles triangle, and BD, the altitude, divides AC, the base, into two equal parts. In other words, AD = DC, and D is the midpoint of AC. Therefore, the x-coordinate of point D is (-8 + 20)/2 = 6, which is also the x-coordinate of point B (notice that we can eliminate choices C, D, and E). Lastly, since AC = BD, and the length of AC is 20 - (-8) = 28, the y-coordinate of point B is the y-coordinate of D plus 28. In other words, the y-coordinate of point B is 0 + 28 = 28. Therefore, the coordinates of point B are (6, 28).
Answer: B
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