Question

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.

>
> Could the hypotenuses of these two triangles lie along the same line?

Answer 1

Yes because they are similar tryangles

Explanation:

Answer 2

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

`(x-0)/(6-0)=(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