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In the rectangular coordinate plane, the coordinates of points A, B, a
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08 Dec 2022, 10:02
08 Dec 2022, 10:02
Expert Reply
00:00
Question Stats:
58% (02:48) correct
41% (02:12) wrong based on 12 sessions
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In the rectangular coordinate plane, the coordinates of points A, B, and C are \((1, 4), (7, 4 + 6 \sqrt{3})\), and \((7, 4)\), respectively. What is the absolute value of the difference between AB and BC ?
\(6 \)
\(4 + \sqrt{3}\)
\(6 − 6 \sqrt{3} \)
\(6 \sqrt{3} − 12 \)
\(12 − 6 \sqrt{3}\)
\(6 \)
\(4 + \sqrt{3}\)
\(6 − 6 \sqrt{3} \)
\(6 \sqrt{3} − 12 \)
\(12 − 6 \sqrt{3}\)
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Re: In the rectangular coordinate plane, the coordinates of points A, B, a
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08 Dec 2022, 23:32
08 Dec 2022, 23:32
1
Expert Reply
To find:- \(|AB-BC|=\)?
\(AB= \sqrt{(7-1)^2+(4 + 6√3-4)^2}=\sqrt{36+108}=\sqrt{144}=12\)
\(BC=\sqrt{(7-7)^2+(4 - 4-6√3)^2}=\sqrt{0+(6√3)^2}=6√3\)
\(|AB-BC|=|12-6√3|\)
Answer: E
\(AB= \sqrt{(7-1)^2+(4 + 6√3-4)^2}=\sqrt{36+108}=\sqrt{144}=12\)
\(BC=\sqrt{(7-7)^2+(4 - 4-6√3)^2}=\sqrt{0+(6√3)^2}=6√3\)
\(|AB-BC|=|12-6√3|\)
Answer: E
Re: In the rectangular coordinate plane, the coordinates of points A, B, a
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
Expert Reply
OE
Draw the points and connect the points to form a right triangle. Subtract the x-coordinate of A from that of C to find the length of AC: 7 − 1 = 6. Subtract the y-coordinate of C from that of B to find the length of BC: \(4 + 6 \sqrt{3}− 4 = 6\). Notice that the ratio of AC to BC is 1 to \(\sqrt{3} \). Therefore, ABC is a 30-60-90 triangle, and the length of AB, the hypotenuse, will be double the length of the shorter side (6), so AB = 12. The absolute value of the difference will be the positive value, obtained by subtracting the smaller value (BC) from the larger value (the length of the hypotenuse, AB):\( AB − BC = 12 − 6 \sqrt{3}\) , which is choice (E).
Draw the points and connect the points to form a right triangle. Subtract the x-coordinate of A from that of C to find the length of AC: 7 − 1 = 6. Subtract the y-coordinate of C from that of B to find the length of BC: \(4 + 6 \sqrt{3}− 4 = 6\). Notice that the ratio of AC to BC is 1 to \(\sqrt{3} \). Therefore, ABC is a 30-60-90 triangle, and the length of AB, the hypotenuse, will be double the length of the shorter side (6), so AB = 12. The absolute value of the difference will be the positive value, obtained by subtracting the smaller value (BC) from the larger value (the length of the hypotenuse, AB):\( AB − BC = 12 − 6 \sqrt{3}\) , which is choice (E).
