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A point R has coordinates (a, b)
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04 Dec 2021, 03:57
04 Dec 2021, 03:57
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66% (02:10) wrong based on 6 sessions
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A point R has coordinates (a, b) whereas point S has coordinates (m, n). If a < 0, and b, m, n > 0, and b > m, then for the line \(l_{1}\) connecting two points R and S:
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 |
Slope of \(l_{1}\) |
0 |
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.
Re: A point R has coordinates (a, b)
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05 Dec 2021, 02:35
05 Dec 2021, 02:35
1
Expert Reply
Since, the x-coordinate a of point R is less than 0 and the y-coordinate b of point R is greater than 0, it means the point R lies in the 2nd quadrant where the x-axis is negative and y-axis is positive.
x-coordinate of point R < 0 implies a < 0
y-coordinate of point R > 0 implies b > 0
Similarly, x-coordinate m and y-coordinate n of the point S are greater than 0, it means the point R lies in the 1st quadrant where both axis are positive.
x-coordinate of point S > 0 implies m > 0
y-coordinate of point S > 0 implies n > 0
However, we are also told that the y-coordinate b of the point R is greater than the y-coordinate n of the point S.
y-coordinate of point R > y-coordinate of point S
a > m
After understanding the placement of both points $R$ and $S$, we can say that the line will go downwards because the point R will be placed higher in the 2nd quadrant as compared to the point S in the 1st quadrant. Therefore, the slope of the line \(\bar{RS}\) will be negative.
Quantity A = Slope of \(l_{1}\), which is negative
Quantity B = 0
Quantity A < Quantity B
Hence, the correct answer is Option B).
x-coordinate of point R < 0 implies a < 0
y-coordinate of point R > 0 implies b > 0
Similarly, x-coordinate m and y-coordinate n of the point S are greater than 0, it means the point R lies in the 1st quadrant where both axis are positive.
x-coordinate of point S > 0 implies m > 0
y-coordinate of point S > 0 implies n > 0
However, we are also told that the y-coordinate b of the point R is greater than the y-coordinate n of the point S.
y-coordinate of point R > y-coordinate of point S
a > m
After understanding the placement of both points $R$ and $S$, we can say that the line will go downwards because the point R will be placed higher in the 2nd quadrant as compared to the point S in the 1st quadrant. Therefore, the slope of the line \(\bar{RS}\) will be negative.
Quantity A = Slope of \(l_{1}\), which is negative
Quantity B = 0
Quantity A < Quantity B
Hence, the correct answer is Option B).
