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).

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