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How many triangles possible?

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refreshment
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How many triangles possible? [#permalink] New post   27 Feb 2009, 05:15
Right triange PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed??

A 110
B 1100
C 9900
D 10000
E 12100



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Re: How many triangles possible? [#permalink] New post   27 Feb 2009, 08:14
E
different variants for x: 4+5+1=10 (4 negative points, 5 positive and zero)
different variants for y: 16-6+1=11 (top coordinate - bottom coor. + 1..can't explain, count with fingers :) )
PR parallel to ox, so we need different variants for x: for 2 points P and Q
PQ parallel to oy, ... P and R
so all possible triagles ... 10*10*11*11 = 12100
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Re: How many triangles possible? [#permalink] New post   27 Feb 2009, 08:23
awesome Q
post505777.html
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JillAdrB
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Re: How many triangles possible? [#permalink] New post   27 Feb 2009, 08:28
oops! i was wrong
C) 9900

10*9*11*10=9900 (for P and R points - same x-coordinate...but for third point 9..if 10 it will be line, not triangle... and the same for y-coord!)
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Re: How many triangles possible? [#permalink] New post   27 Feb 2009, 12:20
Hey can you please explain it clearly. I totally got lost, when you are finding the next 10 and 11. Sorry for the trouble.
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Re: How many triangles possible? [#permalink] New post   28 Feb 2009, 03:33
Even I am missing some combinations not sure where
I am getting only 990...
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Re: How many triangles possible? [#permalink] New post   28 Feb 2009, 13:07
1
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think this way.


assume x values are
(x1,.... x10)
Y values are
(y1,.... y11)


you need three points to form a triangle.

(x1,y1) , (x1,y2) (x2 y1) form a triangle.

--> that means you need to select two points (x1,x2) from x series and two points (y1,y2) from y series.

Select two points from x series = 10P2 (since order does matter.. it should be permuation)
Select two points from y series = 11P2
Answer = 11P2 *10P2 = 11*10 * 10*9 = 9900

I hope you got it.
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Re: How many triangles possible? [#permalink] New post   28 Feb 2009, 17:02
Thanks x2suresh...got it
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abhishekik
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Re: How many triangles possible? [#permalink] New post   02 Mar 2009, 04:22
Nice explanation x2suresh, it is now clear to me.
+1 from me.



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Re: How many triangles possible? [#permalink]
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