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dist: Distances and the Pythagorean Theorem

Exercise template for computing the distance (numeric answer) between two randomly-drawn points in a Cartesian coordinate system.

Name:
dist
Type:
num
Related:
dist2, dist3
Preview:

What is the distance between the two points p=(2,4) and q=(5,4) in a Cartesian coordinate system?

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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?

  • 0 / 1

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?

  • 0 / 1

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.

Description:
Computing the (Euclidean) distance between two randomly-drawn points by using the Pythagorean Theorem.
Solution feedback:
Yes
Randomization:
Random numbers and graphics
Mathematical notation:
Yes
Verbatim R input/output:
No
Images:
Yes
Other supplements:
No
Template:
dist.Rmd
dist.Rnw
Raw: (1 random version)
dist.md
dist.tex
PDF:
dist-Rmd-pdf
dist-Rnw-pdf
HTML:
dist-Rmd-html
dist-Rnw-html

(Note that the HTML output contains mathematical equations in MathML, rendered by MathJax using ‘mathjax = TRUE’. Instead it is also possible to use ‘converter = “pandoc-mathjax”’ so that LaTeX equations are rendered by MathJax directly.)

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")

TEMPLATES
num numeric arithmetic distance Euclidean Pythagoras mathematics