(Euclid 2023, Question 2, CEMC - UWaterloo)

(a) If $Q(5, 3)$ is the midpoint of the line segment with endpoints $P(1, p)$ and $R(r, 5)$, what are the values of $p$ and $r$?
(b) A line with slope $3$ and another line with slope $−1$ intersect at $P(3, 6)$. What is the distance between the $x$-intercepts of the two lines?
(c) For some value of $t$, the line with equation $y = tx + t$ is perpendicular to the line with equation $y = 2x + 7$. Determine the point of intersection of these two lines.

Answer Submission Note(s)
In part (a), separate your answers with a comma.
In part (c), format your answer as "(x,y)".
Separate the answers for each part with a single space.
For example: "p,r n (x,y)"