Proving Diagonals PerpendicularDate: 07/28/2003 at 09:10:05 From: Dan16etta Subject: Perpendicular diagonals Given the points a(-4,1), b(2,3), c (4,9) and d (-2,7), show that quadrilateral abcd is a parallelogram with perpendicular diagonals. Date: 07/28/2003 at 13:35:48 From: Doctor Barrus Subject: Re: perpendicular diagonals First I'm going to draw a rough picture of the four points, so I can see what we're talking about. | * c | d * | | | | | * b | a * | ------------+----------- We want to show that the two diagonals of the quadrilateral are perpendicular. In other words, if we drew a line passing through a and c, and another line passing through b and d, those two lines would be perpendicular to each other. Now how can you tell if two lines are perpendicular? One way, most likely the way you'll want to use here, is to look at their slopes. If the product of two lines' slopes is equal to -1, then the two lines are perpendicular. So let's find the slopes of the two diagonals. rise Slope ac = ------ run 9 - 1 = ---------- 4 - (-4) = 8/8 = 1 Similarly (you'll want to work this out for yourself), the slope of line bd is -1. Now if we take the two slopes and multiply them, we get slope AC * slope BD = 1 * -1 = -1 and since the product is -1, we know that these two lines are perpendicular. Make sense? I hope that helps. If you have further questions, feel free to write back. Good luck! - Doctor Barrus, The Math Forum http://mathforum.org/dr.math/ |
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