Question

On a coordinate plane, 2 polygons are shown. Polygon A B D C has points (negative 5, 2), (negative 3, negative 1), (negative 3, 1), and (negative 1, 2). Polygon A prime B prime D prime C prime has points (negative 3, 3), (1, negative 3), (1, 1), and (5, 3).
Which composition of similarity transformations would map polygon ABDC to polygon A'B'D'C'?

a dilation with a scale factor greater than 1 and then a translation
a dilation with a scale factor greater than 1 and then a rotation
a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation

Answer 1

Dilation with a scale factor greater than 1 and then a translation.

Reason: If you dilate each original point by k about the origin and then translate by (t_x,t_y), we have k(x,y)+(t_x,t_y)=(x',y'). Using A(-5,2)→A'(-3,3) and B(-3,-1)→B'(1,-3) gives k=2 and (t_x,t_y)=(7,-1). Checking C and D also maps correctly, so the transformation is a dilation by 2 followed by the translation (7,-1).