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?
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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?
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)?!
Clarifications made using "y". Now if I can only stump the BATcher!
Another quite hard problem for a maths-rusty brain!
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
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, (y-1)/3 must equal the neg recip of (y-1)/-2 or
(y-1)/3 = 2/(y-1).
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)
Done from a totally different angle (no pun intended). Brilliant KW!