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triangle problem ( alternative concept)

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by rkav » Sat Mar 16, 2013 9:46 am
Problem 75 on page 163 OG 13th edition

Triangle ABC is equilateral and point P is equidistant from the vertices A, B,c. If triangle ABC is rotated clockwise about point P what is the minimum number of degrees the triangle must be rotated so that point B will be in the position where point A is now.

A. 60
b. 120
c. 180
d. 240
e 270

I got the right answer (D but used a different method here. The answer uses relationship of angles within a triangle. I just rotated in halfway (pictured a circle) and knew it had to be more than 180 degrees. Realized it could not be 270 so that left 240.

Is that logic right or did I just get lucky?

Thanks!
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by srcc25anu » Sat Mar 16, 2013 9:53 am
Total angle around Point P = 360 degrees
A, B and C are equidistant from point P (given in question)
if we rotate triangle ABC by 360/3 = 120 degrees, point A will move to current point B, Point B will move to current Point C and C will move to current Point A.
Another rotation by 120 degrees clockwise will take point A to Original Point C, point B to original Point A (Exactly what we are trying to find for this question) and so on. We have rotated twice by 120 degrees and hence a total of 240 degrees from the original position.
Only angle rotations that matter here are 120, 240 and 360 degrees because rotatting by any other degree will not align the 3 vertices to the original vertices.

Instead of a equilateral triangle, if it were a square and point P had been equidistant from the 4 vertices, the only angle rotations we should be bothered about are those at every 360 / 4 = 90 degrees.
so 90, 180, 270 and 360 would have been our concerned rotations.
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by rkav » Sat Mar 16, 2013 10:16 am
Thank you!
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by Anju@Gurome » Sat Mar 16, 2013 10:17 am
rkav wrote:... I just rotated in halfway (pictured a circle) and knew it had to be more than 180 degrees. Realized it could not be 270 so that left 240.

Is that logic right or did I just get lucky?
Your logic is perfectly fine.
For geometry problems in GMAT, it is a good practice to solve them by drawing figures or visualizing the situations.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
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