Answer: Suppose you're given the two points (–2, 1) and (1, 5), and they want you to find out how far apart they are. You can draw in the lines that form a right-angled triangle, using these points as two of the corners. It's easy to find the lengths of the horizontal and vertical sides of the right triangle: just subtract the x-values and the y-values.
Step-by-step explanation: Then use the Pythagorean Theorem to find the length of the third side (which is the hypotenuse of the right triangle):
c2 = a2 + b2
...so:
c
2
=(5−1)
2
+(1−(−2))
2
c = \sqrt{(5 - 1)^2 + (1 - (-2))^2}c=
(5−1)
2
+(1−(−2))
2
c = \sqrt{(4)^2 + (3)^2}c=
(4)
2
+(3)
2
c = \sqrt{16 + 9} = \sqrt{25} = 5c=
16+9
=
25
=5