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31 Dec 2020, 01:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:21) correct
35%
(02:26)
wrong
based on 75
sessions
History
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Time
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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?
I. 3.5
II. 4.0
III. 6.0
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Attachment:
1.png [ 8.66 KiB | Viewed 3668 times ]
31 Dec 2020, 07:06
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Given
To Find
Approach and Working Out
Correct Answer: Option C
- • The figure shows line segment AB and a circle with radius 1 and center (4,2) in the xy-plane.
To Find
- • The values could be the distance between a point on line segment AB and a point on the circle.
Approach and Working Out
- • If we see the figure, we can determine each of the points as shown.
- o The key logic here is to understand that the minimum distance is from the midpoint of AB to the north most point of the circle.
o And the maximum distance is around or the southernmost point to A.
o So these are in between 2 to √17.
Correct Answer: Option C
Attachments
GC1.png [ 51.12 KiB | Viewed 3334 times ]
31 Dec 2020, 07:26
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In the attached screenshot, \(C\) is the center of the circle, and \(D\) is the mid-point of the line segment \(AB\).
Coordinates of point \(D(4,5), E(4,3), G(4,1) \)
We can use the midpoint formula to find the coordinates of point \(D\) i.e. \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\). To find the coordinates of the point \(E\), we can subtract \(1\) unit from the y-axis.
We need to find the distance between \(DE, DG, AG, AE\).
\(DE=\sqrt{(4-4)^2+(5-3)^2}=2\) units.
\(DG=DE+2=5\) units.
Distance between
\(AE = \sqrt{(4-3)^2+(5-3)^2}=\sqrt{5}=2.23\)
\(AG=\sqrt{(4-3)^2+(1-5)^2}=\sqrt{17}=4.12\)
The possible distance between a point on line segment AB and a point on the circle must lie between \(2.23 ≤ x ≤ 4.12\)
Ans C
Coordinates of point \(D(4,5), E(4,3), G(4,1) \)
We can use the midpoint formula to find the coordinates of point \(D\) i.e. \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\). To find the coordinates of the point \(E\), we can subtract \(1\) unit from the y-axis.
We need to find the distance between \(DE, DG, AG, AE\).
\(DE=\sqrt{(4-4)^2+(5-3)^2}=2\) units.
\(DG=DE+2=5\) units.
Distance between
\(AE = \sqrt{(4-3)^2+(5-3)^2}=\sqrt{5}=2.23\)
\(AG=\sqrt{(4-3)^2+(1-5)^2}=\sqrt{17}=4.12\)
The possible distance between a point on line segment AB and a point on the circle must lie between \(2.23 ≤ x ≤ 4.12\)
Ans C
Attachments
Screenshot 2020-12-31 194733.jpg [ 37.3 KiB | Viewed 3257 times ]
