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

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16 Oct 2003, 08:32

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B

C

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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)

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)

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.

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,

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