Question

A triangle has vertices at points (0, 0), (a, b), and (2a, 0). Select all points that lie on the sides of the triangle. A. (a, 0) B. (0, b) C. (–a, b) D. (a/2,b/2) E. (a/3,b/4)

Answer 1

A. (a, 0)

D. (a/2,b/2)

Explanation:

(a, 0) lies on one side of the triangle, because it is between (0,0) and (2a,0)

(0, b) doesn't lie on one side of the triangle, because only the only point with x-coordinate = 0 is (0,0)

(–a, b) doesn't lie on one side of the triangle, because only positive values are valid

Imagine the triangle with vertices (0,0), (a, 0) and (a,b). Let's call β the angle at vertex (0,0)

tan(β) = b/a

For triangle with vertices (0,0), (a/2, 0) and (a/2,b/2)

tan(β) = (b/2)/(a/2) = b/a

then, (a/2,b/2) lies on one side of the triangle

For triangle with vertices (0,0), (a/3, 0) and (a/3,b/4)

tan(β) = (b/4)/(a/3) = (3/4)*(b/a) ≠ b/a

then, (a/3,b/4) doesn't lie on one side of the triangle