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Thread: What's the Point?

20130728, 13:36 #1
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What's the Point?
Points A, B and C are defined by their coordinates in a standard rectangular system of axes. What positive value of y in point B makes triangle ABC a right triangle with AC its hypotenuse?
Last edited by Maudibe; 20130728 at 15:22. Reason: clarify per wisdom of the BATcher

20130728, 14:37 #2
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Afraid it will have to wait until tomorrow, since I have to get up at 05:15 GMT.
But you might like to change the diagram so that the coordinates of B are (4,b)?!Last edited by BATcher; 20130728 at 14:40.
BATcher
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20130728, 15:32 #3
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Clarifications made using "y". Now if I can only stump the BATcher!

20130729, 00:01 #4
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Another quite hard problem for a mathsrusty brain!
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20130729, 22:17 #5
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Damn, you are good! BTW, you can produce a square root symbol in an Excel cell using the Symbol menu on the Insert Tab. Then do a copy/paste: √1000

20130801, 20:53 #6
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Explanation:
In order to make AB perpendicular to BC (to form the right triangle), the slopes of AB and BC must be negative reciprocals of each other.
So, (y1)/3 must equal the neg recip of (y1)/2 or
(y1)/3 = 2/(y1).
Then, "cross multiply" and get: y^2  2y + 1 = 6 and y^2  2y  5 = 0.
Using the quadratic formula: [2 + SQRT(4+20)]/2 which is [2 + sqrt(24)]/2 which is [2+2sqrt(6)]/2
So, the answer is: 1+sqrt(6)

20130801, 21:16 #7
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Done from a totally different angle (no pun intended). Brilliant KW!