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# In the rectangular coordinate plane, the coordinates of points A, B

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
In the rectangular coordinate plane, the coordinates of points A, B  [#permalink]

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31 Oct 2018, 01:25
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Difficulty:

45% (medium)

Question Stats:

66% (02:15) correct 34% (02:34) wrong based on 76 sessions

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In the rectangular coordinate plane, the coordinates of points A, B, and C are (1, 4), (7, 4 + 6√3) and (7, 4), respectively. What is the absolute value of the difference between AB and BC ?

A. 6

B. 4 + √3

C. 6 – 6√3

D. 6√3 – 12

E. 12 – 6√3

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In the rectangular coordinate plane, the coordinates of points A, B  [#permalink]

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31 Oct 2018, 10:29
Bunuel wrote:
In the rectangular coordinate plane, the coordinates of points A, B, and C are (1, 4), (7, 4 + 6√3) and (7, 4), respectively. What is the absolute value of the difference between AB and BC ?

A. 6

B. 4 + √3

C. 6 – 6√3

D. 6√3 – 12

E. 12 – 6√3

To find:- |AB-BC|=?

$$AB= \sqrt{(7-1)^2+(4 + 6√3-4)^2}=\sqrt{36+108}=\sqrt{144}=12$$
$$BC=\sqrt{(7-7)^2+(4 - 4-6√3)^2}=\sqrt{0+(6√3)^2}=6√3$$

$$|AB-BC|=|12-6√3|$$

Ans. (E)
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In the rectangular coordinate plane, the coordinates of points A, B   [#permalink] 31 Oct 2018, 10:29
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