Note: If and intersect at a point , then and

Question 1: Find the point of intersection of the following pairs of lines :

i)   and        ii)   and 

iii)   and 

Answer:

i)       Given   and 

Here Comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines    and  are

ii)      Given   and 

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

iii)    Given  and 

Here comparing with  we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Question 2: Find the coordinates of the vertices of a triangle, the equations of whose sides are:

i) and

ii) and

Answer:

i) Given equations:

     … … … … … i)

     … … … … … ii)

     … … … … … iii)

First consider equations i) and ii):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Now consider equations ii) and iii):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Now consider equations iii) and i):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Therefore the three vertices of the triangle are , ,

ii) Given equations:

     … … … … … i)

     … … … … … ii)

     … … … … … iii)

First consider equations i) and ii):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

 

 

Hence the coordinates of the intersection of the lines  and  are

Now consider equations ii) and iii):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Now consider equations iii) and i):

Here comparing with we get

Similarly,  comparing with we get:

Therefore,

Hence the coordinates of the intersection of the lines  and  are

Therefore the three vertices of the triangle are , ,

Question 3: Find the area of the triangle formed by the lines

i) ,  and

ii) and

iii) and

Answer:

i) Given equations:

     … … … … … i)

     … … … … … ii)

     … … … … … iii)

First consider equations i) and ii):

Here comparing with