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29 May 2018, 22:36
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D
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Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?
A. y = −3x + 4
B. y = −x/3 + 4/3
C. y = −3x + 3/4
D. y = −x/3 + 7/3
E. y = −x/3 − 4
A. y = −3x + 4
B. y = −x/3 + 4/3
C. y = −3x + 3/4
D. y = −x/3 + 7/3
E. y = −x/3 − 4
29 May 2018, 22:45
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Bunuel
Line A is represented by the line y = 3x − 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?
A. y = −3x + 4
B. y = −x/3 + 4/3
C. y = −3x + 3/4
D. y = −x/3 + 7/3
E. y = −x/3 − 4
A. y = −3x + 4
B. y = −x/3 + 4/3
C. y = −3x + 3/4
D. y = −x/3 + 7/3
E. y = −x/3 − 4
Don't need to recall the formulae for perpendicular lines. Just test the answer choices whether they travel through point \((1,2)\).
After checking, we can find out that only \(y = −x/3 + 7/3\) travels through point \((1,2)\).
Answer: D
29 May 2018, 23:40
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Solution
Given:
- • Line A is represented by y = 3x – 4
To find:
- • The equation of the line which is perpendicular to Line A ang travels through point (1, 2)
Approach and Working:
If the equation of Line A is given as y = 3x – 4,
- • Slope of Line A = 3
• Slope of the line perpendicular to Line A = \(\frac{-1}{3}\)
As the perpendicular line passes through (1, 2), we can write
- • \(2 = \frac{-1}{3} * 1 + c\)
Or, \(c = \frac{7}{3}\)
• Therefore, the equation of the line which is perpendicular to line A:
\(y = \frac{-1}{3}x + \frac{7}{3}\)
Hence, the correct answer is option D.
Answer: D
[Note: Obviously answer can also be determined by replacing the value in the given options]
