Consider two right triangles:
1. ΔABC with vertices A(0,0), B(0,2), C(6,0). Then AB is perpendicular to AC and AB=2 units (vertical leg), AC=6 units (horizontal leg).
2. ΔXYZ with vertices X(6,-10), Y(6,0), Z(36,-10). Then XY is perpendicular to XZ and XY=10 units (vrrtical leg), XZ=30 units (horizontal leg).
The equation of the line BC is
\(\dfrac{x-0}{6-0}=\dfrac{y-2}{0-2},\\ \\-x=3y-6,\\ \\x+3y-6=0.\)
Check whether points Y and Z lie on this line:
Y(6,0): \(6+3\cdot 0-6=0\) - true;
Z(36,-10): \(36+3\cdot (-10)-6=0\) - true.
Answer: the hypotenuses of these two triangles could lie along the same line
