Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

An ant is at point A(6,0). Ant starts tarvelling toward the [#permalink]
16 Oct 2003, 07:32

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

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)

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)

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.

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,

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