Two right triangles are graphed on a coordinate plane. one triangle has a vertical side of 2 and a horizontal side of 6. the other triangle has a vertical side of 10 and a horizontal side of 30.
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> could the hypotenuses of these two triangles lie along the same line?

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

Check whether points Y and Z lie on this line:

Y(6,0): - true;

Z(36,-10): - true.

 the hypotenuses of these two triangles could lie along the same line