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A line through points A and B in a coordinate system is graphed by y =

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A line through points A and B in a coordinate system is graphed by y =  [#permalink]

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New post 23 May 2018, 21:50
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (02:42) correct 41% (02:27) wrong based on 124 sessions

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Image
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


Attachment:
CoordinateA.png
CoordinateA.png [ 6.54 KiB | Viewed 1280 times ]

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Re: A line through points A and B in a coordinate system is graphed by y =  [#permalink]

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New post 23 May 2018, 23:23
Bunuel wrote:
Image
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


Attachment:
CoordinateA.png


Let's find the area of the triangle \(AOB\).

Given \(y=−0.5x+2\),
if \(x=0\), then \(y=2\) and if \(y=0\), then \(x=4\)

\(S=0.5*2*4=4\)

So, the area of the triangle \(COD\) must be \(\frac{4}{2}=2\)

Similar technique (check \(x=0\), \(y=0\)) shows that only \(I\) and \(III\) satisfy the given condition (\(S=2\)).

Answer: D
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Re: A line through points A and B in a coordinate system is graphed by y =  [#permalink]

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New post 18 Jan 2020, 06:14
Bunuel @chetn2u
what would be algebraic way to solve this question
I tried to find that since area is the ratio of 1:2
sides would be in the ratio\( 1:\sqrt{2}\)
and formed an equation using two points for C and D
but could not get an equation.
Please help
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Re: A line through points A and B in a coordinate system is graphed by y =  [#permalink]

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New post 18 Jan 2020, 07:40
Bunuel wrote:
Image
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


Attachment:
CoordinateA.png



Given: A line through points A and B in a coordinate system is graphed by y = −0.5x + 2 as shown above.
y-intercept = 2; x-intercept = 4; Area = 4

Asked: 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
y-intercept = 1; x-intercept = 4; Area = 2; OK
II. y = -0.25x + 2
y-intercept = 2; x-intercept = 8; Area = 8; NOT OK
III. y = -x + 2
x-intercept = 2; y-intercept = 2; Area = 2; OK

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

IMO D

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Re: A line through points A and B in a coordinate system is graphed by y =   [#permalink] 18 Jan 2020, 07:40
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