Without using the Pythagoras theorem, show that the points `(4, 4)`, `(3, 5)`and `(1, 1)`are the vertices of a right angled triangle.

Explanation

To show that the points \( A(4, 4) \), \( B(3, 5) \), and \( C(1, 1) \) are the vertices of a right-angled triangle without using the Pythagorean theorem, we can follow these steps:

### Step 1: Check if the points are collinear
To determine if the points are collinear, we can calculate the slopes of the lines formed by the points. If the slopes are not equal, the points are not collinear.

1. **Calculate the slope of line \( AB \)**:
\[
\text{slope of } AB = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 4}{3 - 4} = \frac{1}{-1} = -1
...