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Line l1 has equation x + y = 3 and Line l2 has equation 2x + 2y = 8
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30 Sep 2021, 10:28
30 Sep 2021, 10:28
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62% (01:19) correct
37% (01:28) wrong based on 32 sessions
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Line \(l_1\) has equation \(x + y = 3\) and Line \(l_2\) has equation \(2x + 2y = 8\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Shortest distance between the 2 lines |
\(\frac{1}{2}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Line l1 has equation x + y = 3 and Line l2 has equation 2x + 2y = 8
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30 Sep 2021, 12:42
30 Sep 2021, 12:42
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KarunMendiratta wrote:
Line \(l_1\) has equation \(x + y = 3\) and Line \(l_2\) has equation \(2x + 2y = 8\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Shortest distance between the 2 lines |
\(\frac{1}{2}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Rewriting \(l_1 & l_2\)
\(l_1 : y = 3 - x \)
\(l_2 : 2y = 8 - 2x => y = 4 - x\)
So notice that these 2 are parallel and has slope of -1. Therefore if we consider the line with slope y=x (perpendicular to these two), the points of intersections gives the shortest distance.
line\( y = x\) intersects \(l_1 : y = 3 - x \) at (3/2,3/2)
line\( y = x\) intersects \(l_2 : y = 4 - x \) at (2,2)
So the distance between these 2 points is calculated using the formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
which is \(1/\sqrt{2}\)
Quantity A is larger
Re: Line l1 has equation x + y = 3 and Line l2 has equation 2x + 2y = 8
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10 Nov 2023, 11:43
10 Nov 2023, 11:43
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