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What is the most efficient way to calculate the area of the triangle enclosed in the lines with equation $y= x+2, 2y= -3x + 7$ and $x=5$?

I constructed all the lines and then calculated the sides of the triangle by using Pythagorean theorem.

Thanks in advance.

Anonymous196
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  • Find the points $A$ and $B$ where the other two lines meet $x=5$. The length of $AB$ is the base (you may have to twist your neck a bit). Now compute the height by finding where the other two lines meet. – André Nicolas Mar 31 '16 at 21:40
  • Related: http://math.stackexchange.com/questions/516219/finding-out-the-area-of-a-triangle-if-the-coordinates-of-the-three-vertices-are – mlainz Mar 31 '16 at 21:44
  • http://demonstrations.wolfram.com/TheAreaOfATriangleUsingADeterminant/ using determinants – rtybase Mar 31 '16 at 21:58

2 Answers2

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With that problem? The line x = 5 makes things much easier. Find the coordinates of the vertexes. Make the line x = 5 "the base" and it should be simple enough to find the height.

Generalizing this just a little bit. If you did not have a line that was parallel to the coordinate axes. Find the vertex. Make a rectangle with sides parallel to the coordinate axes, with the vertexes on the rectangle. There are 3 right triangles "in the box" that are not the triangle you are looking for. Calculate the area of the box, and subtract the area of these 3 right triangles.

Doug M
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If you don't want to use the formula for the distance of a point from a line, and only want to use the formula for the distance between two points, you can use Heron's formula.

bartgol
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