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02 May 2021, 06:46
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:29) correct
41%
(01:44)
wrong
based on 97
sessions
History
Date
Time
Result
Not Attempted Yet
Line r passes through points A (-3, 2) and B (0, 0). Which of the following represents a line that is perpendicular to line r?
a) -2/3x + 5y = 9
b) -3/2 + 10y = 18
c) 2x+ 3y = 9
d) 3x+2y = 9
e) 3x -2y = 9
a) -2/3x + 5y = 9
b) -3/2 + 10y = 18
c) 2x+ 3y = 9
d) 3x+2y = 9
e) 3x -2y = 9
02 May 2021, 09:11
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Given: Line r passes through points A (-3, 2) and B (0, 0).
Asked: Which of the following represents a line that is perpendicular to line r?
Equation of line r : y = -2x/3
Equation of line perpendicular to line r : y = 3x/2 + c or 2y - 3x = 2c
IMO E
Asked: Which of the following represents a line that is perpendicular to line r?
Equation of line r : y = -2x/3
Equation of line perpendicular to line r : y = 3x/2 + c or 2y - 3x = 2c
IMO E
02 May 2021, 13:04
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caimanoliveira
I am not sure this is a 600-700-level question, but perhaps I underestimate the number of people who would blunder into a trap answer. There are two key steps to ensuring that you get the correct answer. The first is understanding that the slope of the given line is -2/3:
\(\frac{0 - 2}{0 - -3} = -2/3\)
The second is knowing that a perpendicular line will have a slope of positive 3/2, the reciprocal of the first slope with the opposite sign. Go through the answers one by one to eliminate:
a) -2/3x + 5y = 9
Analysis: Regardless of what happens with x when we move it to the right-hand side, we will then be dividing by 5 (to isolate the y). This will not give us the required slope.
b) -3/2 + 10y = 18
Analysis: I will give this answer choice the benefit of the doubt and assume there is an x after -3/2. Anyway, similar to what we saw above, we know that as soon as we move x to the right-hand side and divide by 10, we will not have the desired slope. We should not have to actually perform the calculation.
c) 2x+ 3y = 9
Analysis: The slope will be negative as soon as we move x to the right-hand side, end of story.
d) 3x+2y = 9
Analysis: Same problem as (C).
e) 3x -2y = 9
Analysis: Yes, this is the only one that will work. A little manipulation gives us
\(-2y = -3x + 9\)
\(y = \frac{3}{2}x - \frac{9}{2}\)
The process can take 30 seconds if you focus on nothing more than the slope, but if you need to spend a little longer to make sure you do not select the first answer that has 3/2 in it, then that is fine.
Good luck with your studies, everyone.
- Andrew
