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# An ant is at point A(6,0). Ant starts tarvelling toward the

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Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
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An ant is at point A(6,0). Ant starts tarvelling toward the [#permalink]  16 Oct 2003, 07:32
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An ant is at point A(6,0). Ant starts tarvelling toward the line A: y = x + 6 along a path so that minimum energy is utilized. Find the distance that Ant travels before it touches line A. (Assume: energy utilized is minimum along the shortest possible path)

A) 7,1
B) 0,6
C) 2,7
D) 7,2
E) 1,7
Intern
Joined: 29 Aug 2003
Posts: 49
Location: Detroit, MI
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Kudos [?]: 2 [0], given: 0

Re: PS: minimum energy [#permalink]  16 Oct 2003, 07:57
0,6

My logic is as follows: Shortest distance between a point and a line is the length of the perpendicular line from that point to the line.

Given y = x + 6

Slope = 1
So, the slope of the perpendicular must be -1 and that line must pass through (6,0). So, the equation should be (y-0) = -1(x-6)
=> y = -x + 6
=> x + y = 6 ........ (2)

Given equation can be rewiteen as -x + y = 6 ........ (1)

Point of intersection is obtained by solving these two equations to give (0,6)
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
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Kudos [?]: 2 [0], given: 0

My guess is E.

Quick way:
The intersecting point has to be on the left of x=6, so A and D are out. You can't get C because it doesn't lie on the original line. B can't be the one because it's distance is longer than E.
SVP
Joined: 03 Feb 2003
Posts: 1607
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Kudos [?]: 85 [0], given: 0

we need to find DISTANCE!

The intersection of y=x+6 and the ant path is (0,6). The distance, therefore, is 6*sqrt 2. Approximately, it is 8.49.

No such option. The closest is D.
CEO
Joined: 15 Aug 2003
Posts: 3467
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Kudos [?]: 718 [0], given: 781

Re: PS: minimum energy [#permalink]  18 Oct 2003, 06:20
Vicky wrote:
An ant is at point A(6,0). Ant starts tarvelling toward the line A: y = x + 6 along a path so that minimum energy is utilized. Find the distance that Ant travels before it touches line A. (Assume: energy utilized is minimum along the shortest possible path)

A) 7,1
B) 0,6
C) 2,7
D) 7,2
E) 1,7

vicks, theres a typo in the question. "distance" is asked but coordinates are given,
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
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i am sorry for the typo. Read question as:

An ant is at point A(6,0). Ant starts tarvelling toward the line A: y = x + 6 along a path so that minimum energy is utilized. Find coordinates of the point that ant touches on reaching line A. (Assume: energy utilized is minimum along the shortest possible path)
A) 7,1
B) 0,6
C) 2,7
D) 7,2
E) 1,7

It is correctly pointed by amar and stolyar that point will be (0,6).
thanks
Manager
Joined: 11 Oct 2003
Posts: 102
Location: USA
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The only points on the line are (0, 6) and (1, 7) from the choices. Figure what is the shortest distance to each..
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