Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are :
Question:
Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are :
(i) $y=x, y=2 x$ and $y+x=6$
(ii) $y=x, 3 y=x, x+y=8$
Solution:
(i) The given equations are
$y=x$....(i)
$y=2 x$...(ii)
$y+x=6$...(iii)
It is seen that the coordinates of the vertices of the obtained triangle are $A(0,0), \mathrm{B}(2,4), \mathrm{C}(3,3)$
(ii) The given equations are
$y=x$....(1)
$3 y=x$...(11)
$x+y=8$....(111)
The two points satisfying (i) can be listed in a table as,
It is seen that the coordinates of the obtained triangle are $A(0,0), B(4,4), C(6,2)$