



 
Hi, What are the coordinates of $s?$ Triangle $sqp$ is a right triangle. What does Pythagoras theorem tell you is the length of the line segment $pq?$ The distance from $p$ to $r$ is 10. What is the distance from $q$ to $r?$ What are the coordinates of $t$ and $r?$ Penny
There are of course two answers, depending on whether Q lies between P and R (which is suggested but not, in my opinion, actually stated.) It's easier that it looks. First draw a reasonably accurate sketch. Now use Pythagoras' Theorem to find the distance PQ. So where would R be? (This depends on a small coincidence that makes the numbers come out nicely, but don't be ashamed to use it; these appear in mathematical "real life" too. To solve a more general problem, you would compute the "direction cosines" \[c_x = (Q_xP_x)/QP\] These are the run and rise of a unit vector in this direction. They are always between 1 and 1, and the sum of their squares is always 1. Multiply by 10 to get the actual run and rise, and add to the coordinates of P to get those of R: \[R_x = P_x + 10 c_x\] ) Good Hunting!  


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