dist: Distances and the Pythagorean Theorem
dist
What is the distance between the two points p=(2,4) and q=(5,4) in a Cartesian coordinate system?
The distance d of p and q is given by d2=(p1−q1)2+(p2−q2)2 (Pythagorean formula).
Hence d=√(p1−q1)2+(p2−q2)2=√(2−5)2+(4−4)2=3.
What is the distance between the two points p=(3,2) and q=(5,5) in a Cartesian coordinate system?
The distance d of p and q is given by d2=(p1−q1)2+(p2−q2)2 (Pythagorean formula).
Hence d=√(p1−q1)2+(p2−q2)2=√(3−5)2+(2−5)2=3.606.
What is the distance between the two points p=(3,2) and q=(4,1) in a Cartesian coordinate system?
The distance d of p and q is given by d2=(p1−q1)2+(p2−q2)2 (Pythagorean formula).
Hence d=√(p1−q1)2+(p2−q2)2=√(3−4)2+(2−1)2=1.414.
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Demo code:
library("exams")
set.seed(403)
exams2html("dist.Rmd", mathjax = TRUE)
set.seed(403)
exams2pdf("dist.Rmd")
set.seed(403)
exams2html("dist.Rnw", mathjax = TRUE)
set.seed(403)
exams2pdf("dist.Rnw")