http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Distance Formula:The distanceA(x 1 ,y 1 )andB(x 2 ,y 2 )isd=
√
(x 1 −x 2 )^2 +(y 1 −y 2 )^2.Example 7:Find the distance between (1, 5) and (5, 2).
Solution:MakeA( 1 , 5 )andB( 5 , 2 ). Plug into the distance formula.
d=√
( 1 − 5 )^2 +( 5 − 2 )^2
=
√
(− 4 )^2 +( 3 )^2
=
√
16 + 9 =
√
25 = 5
You might recall that the distance formula was presented asd=
√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2 , with the first and second
points switched. It does not matter which point is first as long asxandyare both first in each parenthesis. In
Example 7, we could have switchedAandBand would still get the same answer.
d=√
( 5 − 1 )^2 +( 2 − 5 )^2
=
√
( 4 )^2 +(− 3 )^2
=
√
16 + 9 =
√
25 = 5
Also, just like the lengths of the sides of a triangle, distances are always positive.
Know What? RevisitedTo find the length and width of a 52” HDTV, plug in the ratios and 52 into the Pythagorean
Theorem. We know that the sides are going to be a multiple of 16 and 9, which we will calln.
( 16 n)^2 +( 9 n)^2 = 522
256 n^2 + 81 n^2 = 2704
337 n^2 = 2704
n^2 = 8. 024
n= 2. 83