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Question -

Determine graphically the co-ordinates of the vertices of a triangle, the equations of whose sides are :
(i) y = x, y = 2x and y + x = 6 (C.B.S.E. 2000)
(ii) y = x, 3y = x, x + y = 8 (C.B.S.E. 2000)



Answer -

(i) y = x
Substituting some different values of x, we get their corresponding values of y as shown below
 
Now plot the points on the graph and join them. Similarly in the equation y = 2x
 
and y + x = 6 => x = 6 – y
 
Now plot the points on the graph and join them. We see that these lines intersect each other at (0, 0), (3, 3) and (2, 4)
Vertices of the triangle so formed by these lines are (0, 0), (3, 3) and (2, 4)
(ii) y = x, 3y = x, x + y = 8
y = x
Substituting some different values of x, we get corresponding values of y as shown below
 
Plot these points on the graph and join them Similarly in the equation 3y = x
 
and x + y = 8 => x = 8 – y
 
Now plot the points and join them. We see that these lines intersect each other at (0,0), (4, 4), (6, 2)
The vertices of the triangle so formed are (0, 0), (4, 4) and (6, 2)

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