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AC is parallel to the x-axis, it is part of the line y = y1, so the y-coordinate of C is y1.

BC is parallel to the y-axis, it is part of the line x = x2, so the x-coordinate of C is x2.

AC is perpendicular to BC so ACB is a right angle.

Since ABC is a right-angled triangle,

AB2 = AC2 + BC2 (Pythagoras)

Now, AC is a horizontal line so

AC = x2 - x1

BC is a vertical line so BC = y2 - y1


AB2 = (x2 - x1)2 + (y2 - y1)2

Hence the length of AB is

What this means is that

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