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655-705 (Hard)|   Geometry|      
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Bunuel
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A line through points A and B in a coordinate system is graphed by y = 09 Mar 2022, 02:30
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D
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Difficulty:

65% (hard)

Question Stats:

55% (02:46) correct 45% (02:24) wrong based on 62 sessions

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NOTE: Not drawn to scale

A line through points A and B in a coordinate system is graphed by y = −0.5x + 2 as shown above. Which of the following equations will yield the graph of a line through points C and D such that the area of triangle COD will be half the area of triangle AOB?

I. y = -0.25x + 1
II. y = -0.25x + 2
III. y = -x + 2

A. I only
B. II only
C. III only
D. I and III only
E. II and III only


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D
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soudipsengupta
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A line through points A and B in a coordinate system is graphed by y = 15 Mar 2022, 16:29
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Bunuel

NOTE: Not drawn to scale

A line through points A and B in a coordinate system is graphed by y = −0.5x + 2 as shown above. Which of the following equations will yield the graph of a line through points C and D such that the area of triangle COD will be half the area of triangle AOB?

I. y = -0.25x + 1
II. y = -0.25x + 2
III. y = -x + 2

A. I only
B. II only
C. III only
D. I and III only
E. II and III only


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Let us find x and y intercepts of each line:

0) Line AB has intercepts at (4,0) and (0,2). So Area of triangle AOB = (1/2)*4*2=4 square units. As given, area of triangle formed by line CD must be then 2 square units
I) y = -0.25x + 1 has intercepts at (4,0) and (0,1). So Area of triangle COB= (1/2)*4*1=2 square units. TRUE
II) y = -0.25x + 2 clearly not true if (I) is true
III) y = -x + 2 has intercepts at (2,0) and (0,2). So Area of triangle COB= (1/2)*4*1=2 square units. TRUE

So our ANS is D
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Bunuel
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