Answer to Question #305282 in Analytic Geometry for evan

Question

find the value(s) of t so that the distance from P(3,4) to R(t,8) is 4√2

Answer 1

Let us find the values of $t$ so that the distance from $P(3,4)$ to $R(t,8)$ is $4\sqrt{2}.$

It follows that

$\sqrt{(t-3)^2+(8-4)^2}=4\sqrt{2},$

and hence

$(t-3)^2+16=32.$

Therefore, $(t-3)^2=16,$ and thus $t-3=\pm 4.$

We conclude that $t=-1$ or $t=7.$