Question

a triangle has vertices at O (0,0), A(1,0), and B (0,1) a dilation centered at (1,0) is applied to the triangle ? of the sides lie on the same line as their respective images

Answer 1

we know that

when a dilation is applied to the triangle, only the sides AB' and AO' will lies on the same sides of their respective images

therefore

the answer is

two sides

see the attached figure