Find the area of the triangle formed by the lines `y = x, y= 2x, y=3x+4`

Explanation

The equation of sides of the triangle
`y=x`…..`(1)`
`y=2x`……….`(2)`
`y=3x+4`………`(3)`
On solving equations `(1)` and `(2)` , point of intersection`=(0,0)`
On solving equations `(2)` and `(3)` , point of intersection`=(-4,-8)`
On solving equations `(1)` and `(3)` , point of intersection`=(-2,-2)`
Therefore, the vertices of triangle are `(0,0)`, `(-2,-2)` and `(-4,-8)`.
Area of `Delta=(1)/(2)[0(-2+8)-2(-8-0)-4(0+2)]`
`=(1)/(2)(0+16-8)`
`=4` sq. units.