The area of the triangle formed by the graphs of the equations

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The area of the triangle formed by the graphs of the equations x = 0, 2x+3y = 6 and x+y = 3 is :

1. 3 sq. unit
2. 4 1 sq. unit
  2
3. 1 1 sq. unit
  2
4. 1 sq. unit

Correct Option: C

x = 0 ⇒ Equation of y – axis Putting x = 0 in 2x + 3y = 6
0 + 3y = 6 ⇒ y = 2
∴ Co-ordinates of point of intersection on y – axis
= (0, 2)
Again, putting y = 0, x = 3
∴ Point of intersection onx – axis = (3, 0)
In x + y = 3
Putting x = 0, y = 3
and on putting y = 0, x = 3

∴ Required area = ∆OAC – ∆OAB = OCD =	1	× 3 × 3 -	1	× 3 × 2
	2		2

=	9	-	6	=	3
	2		2		2

= 1	1	sq. units
	2

4	1	sq. unit
	2

1	1	sq. unit
	2