Find the coordinates o the vertices of a triangle, the equations of whose sides are: `x+y-4=0,\ 2x-y+3=0\ a n d\ x-3y+2=0`

Explanation

Given: x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0

Let us find the point of intersection of pair of lines. x + y − 4 = 0 … (1)
2x − y + 3 = 0 … (2)
x − 3y + 2 = 0 … (3)
By solving (1) and (2) using cross – multiplication method, we get

`x/(3-4)=y/(-8-3)=1/(-1-2)`

`x=1/3 and y=11/3`

Solving (1) and (3) using cross – multiplication method, we get

`x/(2-12)=y/(-4-2)=1/(-3-1)`

`x=5/2 and y=3/2`

Similarly, solving (2) and (3) using cross – multiplication method, we get

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