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

The hypotenuses could lie along the same line if the triangles are similar.
To find if the if the traingles are similar, figure out whether the ratio of one leg to another is the same. Because the hypotenuse is dependent on the value of the two legs, it's safe to leave them out when trying to determine whether right traingles are similar.
2 to 6 is proportional to 10 to 30
The answer is yes.