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In the xy-plane, the points (5, e) and (f, 7) are on a line t
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19 May 2021, 02:06
19 May 2021, 02:06
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In the xy-plane, the points (5, e) and (f, 7) are on a line that is perpendicular to the graph of the line \(y=-\frac{1}{5}x + 12\). Which of the following represents \(e\) in terms of \(f\)?
A. \(5๐ + 32 \)
B. \(โ5๐ + 32 \)
C. \(5๐ + 25 \)
D. \(-\frac{1}{5} ๐ + 32\)
E. \(\frac{1}{5} ๐ + 32\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(5๐ + 32 \)
B. \(โ5๐ + 32 \)
C. \(5๐ + 25 \)
D. \(-\frac{1}{5} ๐ + 32\)
E. \(\frac{1}{5} ๐ + 32\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: In the xy-plane, the points (5, e) and (f, 7) are on a line t
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19 May 2021, 11:48
19 May 2021, 11:48
1
Carcass wrote:
In the xy-plane, the points (5, e) and (f, 7) are on a line that is perpendicular to the graph of the line \(y=-\frac{1}{5}x + 12\). Which of the following represents \(e\) in terms of \(f\)?
A. \(5๐ + 32 \)
B. \(โ5๐ + 32 \)
C. \(5๐ + 25 \)
D. \(-\frac{1}{5} ๐ + 32\)
E. \(\frac{1}{5} ๐ + 32\)
A. \(5๐ + 32 \)
B. \(โ5๐ + 32 \)
C. \(5๐ + 25 \)
D. \(-\frac{1}{5} ๐ + 32\)
E. \(\frac{1}{5} ๐ + 32\)
Product of the slopes of perpendicular lines is -1
i.e. \((m_1)(m_2) = -1\)
\((\frac{-1}{5})(m_2) = -1\)
\(m_2 = 5\)
Applying slope formula;
\(5 = \frac{(e - 7)}{(5 - f)}\)
\(25 - 5f = e - 7\)
\(e = -5f + 32\)
Hence, option B
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Re: In the xy-plane, the points (5, e) and (f, 7) are on a line t
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01 Jul 2024, 04:30
01 Jul 2024, 04:30
2
โงโงโง Detailed Video Explanation to the Problem โงโงโง
Given that the points (5, e) and (f, 7) are on a line that is perpendicular to the graph of the line \(y=-\frac{1}{5}x + 12\). We need to express e in terms of f.
\(y=-\frac{1}{5}x + 12\)
=> Slope of the line =ย \(-\frac{1}{5}\)
We know that if two lines are perpendicular then product of their slopes = -1
=> Slope of the perpendicular line *ย \(-\frac{1}{5}\) = -1
=> Slope of the perpendicular line = 5
Now, the line passes through the pointsย (5, e) and (f, 7)
=> Slope =ย \(\frac{7 - e}{f - 5}\) = 5
=> 7 - e = 5f - 25
=> e = 32 - 5f = -5f + 32
So, Answer will be B
Hope it helps!
Watch the following video to MASTE Slope of Line
ยญยญ
Given that the points (5, e) and (f, 7) are on a line that is perpendicular to the graph of the line \(y=-\frac{1}{5}x + 12\). We need to express e in terms of f.
\(y=-\frac{1}{5}x + 12\)
=> Slope of the line =ย \(-\frac{1}{5}\)
We know that if two lines are perpendicular then product of their slopes = -1
=> Slope of the perpendicular line *ย \(-\frac{1}{5}\) = -1
=> Slope of the perpendicular line = 5
Now, the line passes through the pointsย (5, e) and (f, 7)
=> Slope =ย \(\frac{7 - e}{f - 5}\) = 5
=> 7 - e = 5f - 25
=> e = 32 - 5f = -5f + 32
So, Answer will be B
Hope it helps!
Watch the following video to MASTE Slope of Line
ยญยญ
