Nothing
sc <- NULL while(is.null(sc)) { p <- c(sample(1:3, 1), sample(1:5, 1)) q <- c(sample(4:5, 1), sample((1:5)[-p[2]], 1)) sol <- sqrt(sum((p - q)^2)) err <- c(sqrt(sum((p + q)^2)), sqrt(sum(abs(p - q)))) err <- err[abs(err - sol) > 0.1] if(length(err) > 1) err <- sample(err, 1) sc <- num_to_schoice(sol, wrong = err, range = c(0.1, 10), delta = 0.3, digits = 3) }
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?
answerlist(sc$questions, markup = "markdown")
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)
$.
\
par(mar = c(4, 4, 1, 1)) plot(0, type = "n", xlim = c(0, 6), ylim = c(0, 6), xlab = "x", ylab = "y") grid(col = "slategray") points(rbind(p, q), pch = 19) text(rbind(p, q), c("p", "q"), pos = c(2, 4)) lines(rbind(p, q)) lines(c(p[1], p[1], q[1]), c(p[2], q[2], q[2]), lty = 2)
answerlist(ifelse(sc$solutions, "True", "False"), markup = "markdown")
extype: schoice
exsolution: r mchoice2string(sc$solutions)
exname: Euclidean distance
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