Find the distance between the points O (0; 0) and A (4; 3).

We have two points: (0; 0) and (4; 3).

Let’s find the distance in two ways.

1) If we imagine that these two points are marked, then one point is the origin of coordinates, and the second is formed like this: “4 units to the right and 3 units up”. That is, the distance between the points is the diagonal of the resulting rectangle and the hypotenuse of the right triangle, which is found:

x ^ 2 = 3 ^ 2 + 4 ^ 2;

x = 5.

2) We use the formula for finding the distance between points:

x ^ 2 = (3 – 0) ^ 2 + (4 – 0) ^ 2;

x = 5.