Determine graphically, the vertices of the triangle formed by the lines

y = x, 3y = x and x + y = 8


Given linear equations are

y = x …(i)


3y = x …(ii)


and x + y = 8 …(iii)


For equation y = x,


If x = 1, then y = 1


If x = 0, then y = 0


If x = 2, then y = 2


Table for line y = x,


x



0



1



2



y



6



1



2



Points



O



A



B



For equation x = 3y,


If x = 0, then y = 0. if x = 3, then y = 1, and if x = 6, then y = 2


Table for line x = 3y,


x



0



3



6



Y



0



1



2



Points



O



C



D



For equation x + y = 8 or x = 8 - y


If x = 0, then y = 8, if x = 8, then y = 0 and if x = 4, then y = 4.


Table for line x + y = 8


x



0



4



8



Y



8



4



0



Points



P



Q



R



Plotting the points A (1, 1) and B(2,2) we get the straight line AB.


Plotting the points C (3, 1) and D(6, 2), we get the straight line CD.


Plotting the point P (0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR.


We see that lines AB and CD intersecting the line PR on Q and D, respectively.



So, is formed by these lines. Hence, the vertices of the formed by the given lines are O(0, 0), Q(4, 4) and D(6,2).


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