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Fold Judgement (Posted on 2013-10-30) Difficulty: 3 of 5
A piece of graph paper is folded once so that (0, 2) coincides with (4, 0) and, (7, 3) coincides with (m, n). Determine (m, n).

See The Solution Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Solution solution Comment 1 of 1

The line defined by (0,2) and (4,0) is y = 2 - x/2.

The fold line is perpendicular to this and so has slope 2, and is y = 2x - 3.

The line connecting point (7,3) with (m,n) has the same -1/2 slope as the first line above: -1/2. The line is y = 13/2 - x/2. Its intersection with y = 2x - 3 can be found:

y = 2x - 3
y = 13/2 - x/2

5y = 23

y = 23/5, x = (38/5)/2 = 19/5

This x value differs from that of (7,3) by 7-19/5 = 3.2, so the desired x value, m, is 19/5 - 3.2 = 3/5 or 0.6 and the y value, n, is 13/2 - 3/10 = 6.2 or 31/5.

So (m,n) = (3/5,31/5) or (0.6,6.2)


  Posted by Charlie on 2013-10-30 22:33:17
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