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16 Oct 2003, 08:32
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N
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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
A) 7,1
B) 0,6
C) 2,7
D) 7,2
E) 1,7
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16 Oct 2003, 08:57
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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)
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)
16 Oct 2003, 10:15
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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.
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.
