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How to find the area of the triangle in the plane R2 bounded by the lines y=x, y=-3x+8 and 3y+5x=0. How can I solve this?

I'm thinking i can take y=x as the origin and just use y=-3x+8 and 3y+5x=0 but how can I convert this to vectors.

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Did you try plotting the lines? Find the intersection points. Two of the lines go through the origin, so you should be able to get one intersection for free! – rschwieb Apr 25 '12 at 22:58
up vote 1 down vote accepted

Here's one solution:

Using the line equations you can find the three vertices of the triangle. After that, you just calculate the determinant and substitute it in the formula to find the area (which is easy because the determinant depends only on the vertices). You can also think of this problem as the half of the vector produt's modulo. When you find the three vertices you find two vectors. With them, you just have to calculate the modulo of their vector product and divide by 2 (and to do that, you also have to calculate a determinant). These interpretations end up being the same thing. Hope it helped.

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