Given equation of lines are `" " 3x-y=3 " " ...(i)`
`" " 2x-3y=2 " " ...(ii)`
and `" " x+2y=8 " " ...(iii)`
Let lines(i), (ii) and (iii) represent the sides of a `DeltaABC` i.e., AB BC and CA, respectively.
On solving lines (i) and (ii), we will get the intersecting point B.
On multiplying Eq. (i) by 3 in Eq. (i) and then subtracting, we get
`{:(9x-3y=9),(ul(underset(-)2x-underset(+)3y=underset(-)2)):}`
`" " 7x=7rArrx=1`
On putting the value of x in Eq. (i) , we get
`3xx1-y=3`
`rArr " " y=0`
So, the coordinate of point of vertex B is (1, 0).
On solving lines (ii) and (iii) , we will get the intersecting point C.
On multiplying Eq. (iii) by a and then subtracting, we get
`{:(2x+4y=16),(ul(underset(-)2x-underset(+)3y=underset(-)2)),(" "7y=14):}`
`rArr " " y=2`
On putting the value of y in Eq. (iii), we get
`" " x+2xx2=8`
`rArr " " x=8-4`
`rArr " " x=4`
Hence , the coordinate of point of vertex C is (4,2).
On solving lines (iii) and (i), we will get the intersecting point A.
On multiplying in Eq. (i) by 2 and then adding Eq. (iii) , we get
`{:(6x-2y=6),(ul(x+2y=8)),(7x=14):}`
`rArr " " x=2`
On putting the value of x in Eq. (i), we get
`3xx2-y=3`
`rArr " " y=6-3`
`rArr " " y=3`
So, the coordinate of point of vertex A is (2, 3).
Hence, the vertices of the `DeltaABC` formed by the given lines are A(2, 3), B(1, 0) and C(4,2).
