in a XY plane, the coordinates of a triangle ABC are (1,1), (2,6) and (5,4). what is the area of the triangle?
how do i approach to this kinda problem
kinds regards
Nafi
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coordinate geometry
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nafiul9090
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Brent@GMATPrepNow
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The trick is to draw a rectangle around the points and find the area of this rectangle.nafiul9090 wrote:in a XY plane, the coordinates of a triangle ABC are (1,1), (2,6) and (5,4). what is the area of the triangle?
From this area subtract the areas of the 3 right triangles that surround the target triangle.
See attachment
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truplayer256
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Plot the points and then connect the three dots. One of the best ways in my opinion to come up with the area of the triangle is to enclose a rectangle around it and subtract the area of the 3 different right triangles that you get. In this case, you get the following:
Area of rectangle = 4*5 = 20 units^2
Area of right triangle 1 = (1/2)(2)(3) = 3 units^2
Area of right triangle 2 = (1/2)(5)(1) = 2.5 units^2
Area of right triange 3 = (1/2)(4)(3) = 6 units^2
Therefore the area of the triangle is 20 - (9 + 2.5) = 8.5 units^2
Area of rectangle = 4*5 = 20 units^2
Area of right triangle 1 = (1/2)(2)(3) = 3 units^2
Area of right triangle 2 = (1/2)(5)(1) = 2.5 units^2
Area of right triange 3 = (1/2)(4)(3) = 6 units^2
Therefore the area of the triangle is 20 - (9 + 2.5) = 8.5 units^2
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nafiul9090
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Brent@GMATPrepNow
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Difficulty-level questions are always somewhat contentious, since there will always be someone who wants others to know that he/she thinks the solution is easy.nafiul9090 wrote:what would be the level of this question??
I have posed a question similar to this in a classroom setting to hundreds of students, and I can tell you that about 10% are able to answer it (in 2 minutes).
Given this, I believe that this is an 80-100 percentile question. In "total score" parlance, I think it's a 650+ question.
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pemdas
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This problem can be easily solved if we use the vector product rule. We first, find the difference between one point and two other points, and then find the vector product. The whole work is also derived algebraically to avoid matrix manipulations such as S=|(Xâ‚�-X₃)"¢(Yâ‚‚-Y₃)-(Xâ‚‚-X₃)"¢(Yâ‚�-Y₃)|/2 where A(Xâ‚�, Yâ‚�), B(Xâ‚‚, Yâ‚‚) и C(X₃, Y₃) are three different points.
Hence S=|(1-5)*(6-4) - (2-5)*(1-4)|/2 = 17/2 = 8.5
Hence S=|(1-5)*(6-4) - (2-5)*(1-4)|/2 = 17/2 = 8.5
nafiul9090 wrote:in a XY plane, the coordinates of a triangle ABC are (1,1), (2,6) and (5,4). what is the area of the triangle?
how do i approach to this kinda problem
kinds regards
Nafi
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