Perpendicular lines

The triangle $PQR$ is isosceles, with $PR = QR$. $P$ is $(1,5)$ and $Q$ is $(5,1)$. $ ngle PRQ$ is not a right angle. Determine the coordinates of one possible location for $R$.

May/June 2021

$A$ lies at $(3,11)$ and $B$ lies at $(-5,-5)$. Line $L$ has equation $2y + x = 5$.

May/June 2023

The equation for line $L$ is $5y+3x=10$.

May/June 2025

On the grid, the points $P$ and $Q$ together with line $L$ are displayed.

Oct/Nov 2019

$A$ has coordinates $(-2, 3)$ and $B$ has coordinates $(4, 5)$.

Oct/Nov 2021

$P$ denotes the point $(-1,4)$, while $Q$ denotes the point $(-3,-2)$.

Oct/Nov 2024