Question

The sides of a triangle are $y=x,y=2x$ and $y=3x+4$. Find the area of the triangle in sq.units

Answer 1

Given:

$y=x$ ........(1)

$y=2x$ ..........(2)

$y=3x+4$ ........(3)

From(1) and (2) $x=0andy=0$

put $y=2x$ in (3)

we get $x=-4$

put value $x=-4$ in equation(2)

$\therefore y=8$

Solving(2) and (3) we get $x=-2,y=-2$

So the vertices of triangle:$(0,0),(-4,-8),(-2,-2)$

Since one vertex is at the origin the area of the triangle is

$\frac{1}{2}(x_1{y}_2-x_2{y}_1)=\frac{1}{2}[-4(-2)-(-2\left)\right(-8\left)\right]=4$ sq. units.