Results 1 to 7 of 7
Thread: What's the Point?

20130728, 14:36 #1
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,637
 Thanks
 115
 Thanked 650 Times in 592 Posts
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 16:22. Reason: clarify per wisdom of the BATcher

20130728, 15:37 #2
 Join Date
 Feb 2008
 Location
 A cultural area in SW England
 Posts
 3,417
 Thanks
 33
 Thanked 195 Times in 175 Posts
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 15:40.
BATcher
Time prevents everything happening all at once...

20130728, 16:32 #3
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,637
 Thanks
 115
 Thanked 650 Times in 592 Posts
Clarifications made using "y". Now if I can only stump the BATcher!

20130729, 01:01 #4
 Join Date
 Feb 2008
 Location
 A cultural area in SW England
 Posts
 3,417
 Thanks
 33
 Thanked 195 Times in 175 Posts
Another quite hard problem for a mathsrusty brain!
BATcher
Time prevents everything happening all at once...

20130729, 23:17 #5
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,637
 Thanks
 115
 Thanked 650 Times in 592 Posts
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, 21:53 #6
 Join Date
 Jan 2001
 Location
 La Jolla, CA
 Posts
 1,470
 Thanks
 30
 Thanked 62 Times in 58 Posts
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, 22:16 #7
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,637
 Thanks
 115
 Thanked 650 Times in 592 Posts
Done from a totally different angle (no pun intended). Brilliant KW!