Question

Does anyone know the answer?

Answer 1

`(27)/(14)\ un^2.`

Explanation:

Plot the graphs of the given lines on hte coordinate plane (see attached diagram).

These three lines form triangle ABC.

1. Find the length of AC:

Point A has coordinates (0,0), point C has coordinates (0,3) {point of intersection of the line
`y=-(4)/(3)x+3` with y-axis}. Hence,

`AC=|3-0|=3\ units`

2. Find the distance from point B to the y-axis:

First, find the coordinates of the point B:

`y=x\\ \\y=-(4)/(3)x+3\Rightarrow x=-(4)/(3)x+3,\ \ (7)/(3)x=3,\ \ x=y=(9)/(7)`

And point B has coordinates
`\left((9)/(7),(9)/(7)\right)`

So,

`h=(9)/(7)\ units`

3. Find the area of the triangle ABC:

`A_(ABC)=(1)/(2)AC\cdot h=(1)/(2)\cdot 3\cdot (9)/(7)=(27)/(14)\ un^2.`