In flaviobarros/exams: Automatic Generation of Exams in R

p <- c(sample(1:3, 1), sample(1:5, 1))
q <- c(sample(4:5, 1), sample(1:5, 1))
sol <- sqrt(sum((p - q)^2))

Question

What is the distance between the two points $p = (r p[1], r p[2])$ and $q = (r q[1], r q[2])$ in a Cartesian coordinate system?

Solution

The distance $d$ of $p$ and $q$ is given by $d^2 = (p_1 - q_1)^2 + (p_2 - q_2)^2$ (Pythagorean formula).

Hence $d = \sqrt{(p_1 - q_1)^2 + (p_2 - q_2)^2} = \sqrt{(r p[1] - r q[1])^2 + (r p[2] - r q[2])^2} = r round(sol, digits = 3)$. \

par(mar = c(4, 4, 1, 1))
plot(0, type = "n", xlim = c(0, 6), ylim = c(0, 6), xlab = "x", ylab = "y")
grid(col = "slategray")
points(rbind(p, q), pch = 19)
text(rbind(p, q), c("p", "q"), pos = c(2, 4))
lines(rbind(p, q))
lines(c(p[1], p[1], q[1]), c(p[2], q[2], q[2]), lty = 2)