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 07-12-2012, 03:06 AM #1 Junior Member   Join Date: Nov 2010 Posts: 152 Math problem An iscoceles triangle is in the xy plane. The hypotenuse line segment has a slope of a, where a>2. What is the product of the three line segments' slopes? 1/a -a a A^2 0 Reply
 07-12-2012, 05:23 AM #2 Member   Join Date: Mar 2011 Location: Staten Island, NY Posts: 915 I assume you mean an isosceles right triangle since only right triangles have a hypotenuse. Then the two legs are perpendicular. This means that their slopes are negative reciprocals of each other. So the product of their slopes is -1. Therefore the product of the three slopes is (-1)a = -a. Extra detail: If one of the legs has slope b, then the other leg has slope -1/b. So the product of the three slopes is b(-1/b)(a) = -a. Technical note: This is not really a good problem. There is actually the possibility that the product is undefined. If the legs are parallel to the coordinate axes, then the vertical segment has an undefined slope. So clearly this is not an actual SAT question. Reply
 07-12-2012, 12:13 PM #3 Junior Member   Join Date: Nov 2010 Posts: 152 Yes, I meant an iscoceles right triangle. I think they avoided it by the >2 part. Thanks Reply
 07-12-2012, 03:14 PM #4 Member   Join Date: Mar 2011 Location: Staten Island, NY Posts: 915 You are right. I missed that. If the legs are parallel to the coordinate axes, then the slope of the hypotenuse will be 1 or -1. Reply
 07-12-2012, 03:18 PM #5 Junior Member   Join Date: Apr 2012 Posts: 255 Yeah, im pretty sure thats not a right triangle then. It would make it a lot easier to know one of yhe side lenghts but I aldo dont really understand your statements below. Sent from my SGH-T959V using CC Reply
 07-12-2012, 10:31 PM #6 Junior Member   Join Date: Sep 2011 Posts: 68 nvm 10char Reply
 07-13-2012, 02:29 AM #7 Senior Member   Join Date: Mar 2012 Location: Cambridge, MA Posts: 1,913 Problem's a little unclear...a could be infinitely large. If a is a finite number, the other two legs are perpendicular, so the product of their slopes is -1. Therefore the product of all three slopes is -a. Reply

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