http://www.thearealist.com/triangle-area/finding-the-area-of-a-triangle-based-on-vertices-lines Fri, 03 Feb 2012 13:07:59 -0500 http://wordpress.org/?v=2.8.4 hourly 1 http://www.thearealist.com/triangle-area/finding-the-area-of-a-triangle-based-on-vertices-lines/comment-page-1#comment-1367 Brian Mon, 30 Nov 2009 13:15:59 +0000 http://www.thearealist.com/triangle-area/finding-the-area-of-a-triangle-based-on-vertices-lines#comment-1367 -3x+y=4, and 2x+y=4 intersect at (0,4), call that point A x-2y=2 and 2x+y=4 intersect at (2,0), call that point B x-2y=2 and -3x+y=4 intersect at (-2,-2), call that point C Side AB is on line 2x+y=4, which has slope -2 Side BC is on line x-2y=2, which has slope 1/2 AB and BC are perpendictular (-2 * 1/2 = -1) The length of AB is sqrt[20] The length of BC is sqrt[20] The area of ABC is sqrt[20] * sqrt[20] / 2 = 10<br><b>References : </b><br> -3x+y=4, and 2x+y=4 intersect at (0,4), call that point A
x-2y=2 and 2x+y=4 intersect at (2,0), call that point B
x-2y=2 and -3x+y=4 intersect at (-2,-2), call that point C
Side AB is on line 2x+y=4, which has slope -2
Side BC is on line x-2y=2, which has slope 1/2
AB and BC are perpendictular (-2 * 1/2 = -1)
The length of AB is sqrt[20]
The length of BC is sqrt[20]
The area of ABC is sqrt[20] * sqrt[20] / 2 = 10
References :

]]> http://www.thearealist.com/triangle-area/finding-the-area-of-a-triangle-based-on-vertices-lines/comment-page-1#comment-1366 sahsjing Mon, 30 Nov 2009 12:25:59 +0000 http://www.thearealist.com/triangle-area/finding-the-area-of-a-triangle-based-on-vertices-lines#comment-1366 Draw all three lines on x-y plane, and find all intersection points: (0,4), (2,0) and (-2,-2). Since the triangle can be split into two triangles with a common base = 2+4/3 = 10/3, the area is equal to (1/2)(10/3)(4+2) = 10 units^2 --------- Attn: Try to find to simpler way to get it done.<br><b>References : </b><br> Draw all three lines on x-y plane, and find all intersection points: (0,4), (2,0) and (-2,-2).
Since the triangle can be split into two triangles with a common base = 2+4/3 = 10/3, the area is equal to
(1/2)(10/3)(4+2) = 10 units^2
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Attn: Try to find to simpler way to get it done.
References :

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