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18 Feb 2015, 02:29
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (03:06) correct
49%
(02:52)
wrong
based on 210
sessions
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Not Attempted Yet
The line k has a positive slope m and it passes through the point (-4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
A. 1/4
B. 3/4
C. 5/4
D. 7/4
E. cannot be determined
A. 1/4
B. 3/4
C. 5/4
D. 7/4
E. cannot be determined
Updated on: 15 Jul 2020, 11:17
Originally posted by BrushMyQuant on 18 Feb 2015, 07:02.
Last edited by BrushMyQuant on 15 Jul 2020, 11:17, edited 1 time in total.
Last edited by BrushMyQuant on 15 Jul 2020, 11:17, edited 1 time in total.
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(Figure attached)
Equation of line will be given by
y-6 / (x- (-4)) = m
or, y = mx + 4m + 6
Area of triangle formed by line k and x and y-axis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given)
Simplifying we will get
16m^2 + 48m + 36 = 108m
=> 16m^2 - 60m + 36 = 0
=> 4m^2 - 15m + 9 = 0
=> 4m^2 - 12m - 3m + 9 =0
=> 4m ( m-3) -3 (m-3) = 0
=> m = 3 , 3/4
So, answer will be B
Hope it helps!
Equation of line will be given by
y-6 / (x- (-4)) = m
or, y = mx + 4m + 6
Area of triangle formed by line k and x and y-axis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given)
Simplifying we will get
16m^2 + 48m + 36 = 108m
=> 16m^2 - 60m + 36 = 0
=> 4m^2 - 15m + 9 = 0
=> 4m^2 - 12m - 3m + 9 =0
=> 4m ( m-3) -3 (m-3) = 0
=> m = 3 , 3/4
So, answer will be B
Hope it helps!
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File comment: Figure
figure.png [ 35.81 KiB | Viewed 9458 times ]
18 Feb 2015, 08:28
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I am not sure if my way of approach is correct. But still I ended up with the answer..
Area of the triangle formed by the line k with X & Y axis is 54.
1/2 * Base * Height = 54
Here Base refers to the x-intercept in units and Height refers to the y-intercept in units
So --> X (or Base) * Y (or Height) = 108
We know that the line k passes through the point (-4,6) and has a positive slope.
Therefore, the point where the line meets the X-axis must be definitely greater than -4 i.e greater than 4 units from the origin(Base)
Similarly, the point where the line meets the Y-axis must be definitely greater than 6 i.e greater than 6 units from the origin(height)
There are a handful of factors that multiply into 108 but only one satisfies the above condition.
9 and 12 -- valid since it satisfies both of the above criteria
the below ones do not
27 and 4
18 and 6
36 and 3
108 and 1
So the y intercept can be either (0,12) or (0,9)
and x-intercept can be either (-9,0) or (-12,0)
We slope m = (y2-y1)/(x2-x1) --> 12/9 or 9/12 i.e 4/3 or 3/4
Answer is 3/4 (B)
Area of the triangle formed by the line k with X & Y axis is 54.
1/2 * Base * Height = 54
Here Base refers to the x-intercept in units and Height refers to the y-intercept in units
So --> X (or Base) * Y (or Height) = 108
We know that the line k passes through the point (-4,6) and has a positive slope.
Therefore, the point where the line meets the X-axis must be definitely greater than -4 i.e greater than 4 units from the origin(Base)
Similarly, the point where the line meets the Y-axis must be definitely greater than 6 i.e greater than 6 units from the origin(height)
There are a handful of factors that multiply into 108 but only one satisfies the above condition.
9 and 12 -- valid since it satisfies both of the above criteria
the below ones do not
27 and 4
18 and 6
36 and 3
108 and 1
So the y intercept can be either (0,12) or (0,9)
and x-intercept can be either (-9,0) or (-12,0)
We slope m = (y2-y1)/(x2-x1) --> 12/9 or 9/12 i.e 4/3 or 3/4
Answer is 3/4 (B)
