## Euclid 2023 Question 2, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with euclid, euclid23, highschool.

**(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)"

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