Question

Find the distance between (3, 8) and (7, -11). Round to the nearest hundredth.

Answer 1

Let's call these two points A(3,8) and B(7,-11). Construct a right triangle using the A and B, the line between the points being the hypotenuse of the triangle (the orientation of the triangle doesn't really matter).

That gives you the length of two perpendicular sides b and c as
b = |7 - 3| and
c = |-11 - 8|
or b=4 and c=19

Pythagoras says \[a ^{2}=b^{2}+c^{2}\] so
\[a^{2} = 4^{2} + 19^{2}\]
or \[a^{2} = 377\]which means
\[a = \sqrt{377} = 19.4164\]
rounded to the nearest hundredth is 19.42.
The hypotenuse in this case is the shortest line between the two points, so its length is the distance between the points.