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

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Senior Manager
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An ant is at point A(6,0). Ant starts tarvelling toward the [#permalink] New post 16 Oct 2003, 07:32
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A
B
C
D
E

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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
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Re: PS: minimum energy [#permalink] New post 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
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 [#permalink] New post 16 Oct 2003, 09:15
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.
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 [#permalink] New post 18 Oct 2003, 04:58
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.
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Re: PS: minimum energy [#permalink] New post 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
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 [#permalink] New post 19 Oct 2003, 00:44
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
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 [#permalink] New post 20 Oct 2003, 19:16
The only points on the line are (0, 6) and (1, 7) from the choices. Figure what is the shortest distance to each..
  [#permalink] 20 Oct 2003, 19:16
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