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The figure shows line segment AB and a circle with radius
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07 Sep 2020, 04:52
07 Sep 2020, 04:52
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68% (02:09) correct
31% (02:56) wrong based on 38 sessions
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GRE The figure shows line segment AB.png [ 8.66 KiB | Viewed 3883 times ]
The figure shows line segment AB and a circle with radius 1 and center (4,2) in the xy-plane. Which of the following values could be the distance between a point on line segment AB and a point on the circle?
Indicate all such values.
A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5
F. 4.0
G. 4.5
H. 5.0
I. 5.5
J. 6.0
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Official Answer
B,C,D,E,F
Re: The figure shows line segment AB and a circle with radius
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08 Sep 2020, 05:37
08 Sep 2020, 05:37
1
I don't know if this is the right way to go but I tried to evaluate the minimum distance and the max distance.
A few things first. We know that the middle of segment AB and the center of the circle are vertically aligned (compute the coordinates of the middle you'll see its x-coordinate is 4 too and y-coordinate is 5).
So the minimum distance is if we linked the middle of AB and the top of the circle. That's a distance of 2.
Now the maximum distance is obtained if we linked one end of the segment AB and the lowest point of the circle. Let's compute the distance.
A has coordinates (3,5) and the lowest point of the circle has coordinates (4,1). So the distance is \(\sqrt{(-1)^2 + 4^2}=\sqrt{17}\) which is around 4.12. So we tick all the answers between.
A few things first. We know that the middle of segment AB and the center of the circle are vertically aligned (compute the coordinates of the middle you'll see its x-coordinate is 4 too and y-coordinate is 5).
So the minimum distance is if we linked the middle of AB and the top of the circle. That's a distance of 2.
Now the maximum distance is obtained if we linked one end of the segment AB and the lowest point of the circle. Let's compute the distance.
A has coordinates (3,5) and the lowest point of the circle has coordinates (4,1). So the distance is \(\sqrt{(-1)^2 + 4^2}=\sqrt{17}\) which is around 4.12. So we tick all the answers between.
Re: The figure shows line segment AB and a circle with radius
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08 Sep 2020, 10:57
08 Sep 2020, 10:57
1
Quote:
Which of the following values could be the distance between a point on line segment AB and a point on the circle?
Step 1: Understanding the question
When point C is the mid point of line segment AB, then CD is the minimum distance and AE is the maximum distance between a point on line segment AB and a point on the circle.
Step 2: Calculation
Coordinate of point C, which is mid point of AB = (4,5)
Coordinate of point D = (4,3)
Coordinate of point E = (4,1)
Minimum distance ie CD = 2
Applying pythagoras th. to find Maximum distance ie AE = \(\sqrt{AC^2+CE^2}\) =\(\sqrt{ 1+4^2}\) = \(\sqrt{17}\)
Hence, B,C,D,E,F is correct
Attachments
Untitled.png [ 35.18 KiB | Viewed 3771 times ]
