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# co-ordinate geometry problem

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co-ordinate geometry problem [#permalink]  21 Mar 2011, 21:40
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60% (01:49) correct 40% (00:34) wrong based on 1 sessions
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?
A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0
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Re: co-ordinate geometry problem [#permalink]  21 Mar 2011, 21:53
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First plot the line. The y intercept is (0,-3) the x intercept is (4,0)
The height of the triangle formed by the triangle with vertices (0,0),(0,-3),(4,0) is say h. It's area is 1/2*3*4=6. the hyp of the triangle is 5 (triplet 3:4:5).
Therefore 1/2*h*5=6 hence h =12/5=2.4
Now the min distaff between the circle and line is 2.4-radius. Radius is 1. Hence min distance is 1.4. A is the answer
asmit123 wrote:
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?
A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0

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Posts: 52
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Kudos [?]: 1 [0], given: 4

Re: co-ordinate geometry problem [#permalink]  21 Mar 2011, 22:32
Thanks friend. That was very clear.
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Re: co-ordinate geometry problem [#permalink]  22 Mar 2011, 01:14
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Re: co-ordinate geometry problem [#permalink]  22 Mar 2011, 02:52
Excellent explanation gmat1220.

+1 to you.
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Re: co-ordinate geometry problem [#permalink]  22 Mar 2011, 08:32
gmat1220 wrote:
First plot the line. The y intercept is (0,-3) the x intercept is (4,0)
The height of the triangle formed by the triangle with vertices (0,0),(0,-3),(4,0) is say h. It's area is 1/2*3*4=6. the hyp of the triangle is 5 (triplet 3:4:5).
Therefore 1/2*h*5=6 hence h =12/5=2.4
Now the min distaff between the circle and line is 2.4-radius. Radius is 1. Hence min distance is 1.4. A is the answer
asmit123 wrote:
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y=(3/4)x -3 ?
A:1.4
b:sqrt of 2
c:1.7
d:sqrt of 3
e:2.0

Posted from my mobile device

Good Post thanks gmat1220
Re: co-ordinate geometry problem   [#permalink] 22 Mar 2011, 08:32
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