A general solution to find the distance between two points A and B:

Let the coordinates of A be (x1, y1) and let the coordinates of B be (x2, y2). Then, the distance between the two points A and B is:

[(y1 - y2) ^ 2 + (x1 - x2) ^ 2 ] ^ 0.5

Why this is always true is explained in the picture, part a. This result is because of the use of the Pythagoras' theorem.

To show that triangle PQR is a right-angled triangle, there are several ways to do this. One is to draw out the graph and measure the angle PQR which is 90 degrees. Hence, triangle PQR is a right-angled triangle. Another way is to note that the three sides of the triangle form a Pythagorean triplet, as written in the picture, part b. This method is probably the suggested method since the first part asked for the sides of the triangle. This method is how we can quickly verify a triangle with sides 3 units, 4 units, and 5 units must form a right-angled triangle, since (3,4,5) forms a Pythagorean triplet i.e. 3^2 + 4^2 = 5^2

This is based on vectors and how it is viewed on a cartesian plane. Which is ax and y axis