Question

What is the distance between the points (4, 7) and (4, 5)?

Answer 1

Those two points lie on a vertical line since the x coordinate is the same for both. So the distance is just the difference between the two y coordinates, which is 2.

If there were not along a vertical or horizontal line, then you can draw them on a two dimensional graph, draw a line between the two points, have that line as the hypotenuse of a right angle triangle where you form the two right angled sides by drawing horizontal and vertical lines from the two points, get the length of those two sides, and then use Pythagoras's theorem for solving the length of the hypotenuse.