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?No, because they are not similar trianglesNo, because one is larger than the otherYes, because they are both right trianglesYes, because they are similar triangles Description
Accepted Solution
A:
Answer: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.Answer: the hypotenuses of these two triangles could lie along the same line