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Question from T., a student:

how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x-3y-17=0,4x-9y+13=0?

Hi,

Each pair of lines intersects at a point which is a vertex of the triangle, hence you need to solve each pair of lines for the coordinates of the vertex. For example with lines 1 and 2 you have

4x+3y+1=0
4x-3y-17=0

I would add the two equations to get

8x - 16 = 0

so

x = 2.

Substitute x = 2 into equation 1 to find y = -3 and hence one vertex is (2, -3).

Find the intersection of lines 2 and 3 and then lines 1 and 3.

Harley

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