write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{4}$, centered at the…

1. First, recall the formula for dilation centered at the origin:
   • If a point ((x,y)) is dilated with a scale - factor (k) centered at the origin, the new coordinates ((x',y')) are given by ((x',y')=(k x,k y)).
2. Assume the coordinates of point (R) are ((x_R,y_R)), point (S) are ((x_S,y_S)), and point (T) are ((x_T,y_T)). From the graph, we can see that (R(- 8,-8)), (S(-8,8)), and (T(0,-8)).
   • For point (R):
     • The scale - factor (k = \frac{1}{4}). Using the dilation formula ((x',y')=(k x,k y)), where (x=-8) and (y = - 8).
     • (x_R'=\frac{1}{4}\times(-8)=-2) and (y_R'=\frac{1}{4}\times(-8)=-2). So, (R'(-2,-2)).
   • For point (S):
     • Here (x=-8) and (y = 8), and (k=\frac{1}{4}).
     • (x_S'=\frac{1}{4}\times(-8)=-2) and (y_S'=\frac{1}{4}\times8 = 2). So, (S'(-2,2)).
   • For point (T):
     • Here (x = 0) and (y=-8), and (k=\frac{1}{4}).
     • (x_T'=\frac{1}{4}\times0 = 0) and (y_T'=\frac{1}{4}\times(-8)=-2). So, (T'(0,-2)).

Answer:

(R'(-2,-2)), (S'(-2,2)), (T'(0,-2))