Question

A right triangle is formed by the origin and the x- and y-intercepts of the line `11x - 4y = 22`. What is the area of the triangle?

Answer 1

`A = 11/2 "units"^2`

Explanation:

To calculate the area of the triangle, we need to know the intercepts of the line `11x - 4y = 22` and the axis.

Let's transform the equation first:

`11x - 4y = 22<=> y = 11/4 x - 11/2`

What is the intercept with the `y` axis?

We can find out if we plug `x = 0` in the equation:
`y = - 11/2`

So, the intercept with the `y` axis is `(0, -11/2)`

What is the intercept with the `x` axis?
We can find out if we plug `y = 0` in the equation:
`11/4x - 11/2 = 0 <=> x = 2`

So, the intercept with the `x` axis is `(2, 0)`.

By the way, our triangle looks like this:
graph{y = 11/4 x - 11/2 [-7.34, 8.464, -6.8, 1.1]}

Because of the intercepts, we know that the length of one leg is `a = 11/2` and the length of the other one is `b = 2`.

Now, we can compute the area of the triangle with the formula `A = 1/2 a b`:

`A = 1/2 * 11/2 * 2 = 11/2 "units"^2`