Triangle BC has vertices A(1,1), B(2.5,3), and C(0,-3). It is dilated by a scale factor of 1-2 about the origin to create triangle A'B'C'. What is the length, in units, of side B'C'

Question

Triangle BC has vertices A(1,1), B(2.5,3), and C(0,-3). It is dilated by a scale factor of 1-2 about the origin to create triangle A'B'C'. What is the length, in units, of side B'C'

Answer 1

Assuming you meant a scale factor of 1:2 vice 1-2, then triangle A'B'C' is twice as big as triangle ABC (triangle ABC is the 1, triangle A'B'C' is the 2). That means that side B'C' is twice as long as side BC. Use the distance formula to compute the length of side BC:

Length of BC = √[(x_C-x_B)²+(y_C-y_B)²]

Length of B'C' = 2·BC