George has a triangle-shaped garden in his backyard. he drew a model of this garden on a coordinate grid with vertices a(4,2), b(2,4), c(6,4) he wants to create anothe, similar-shaped garden, a’b’c , by dilating triangle abc by a scale factor of 0.5. what are coordinates of a’b’c’

The coordinates of A’B’C’ are:

                  A'(2,1)

                  B'(1,2)

                  C'(3,2)

The vertices of the triangle shaped garden is given by:

        A(4,2), B(2,4), C(6,4)

As we know that if a figure is dilated by a fixed scale factor than each of the vertices also get multiplied by the same factor.

i.e. if any figure with a vertex as A(a,b) is dilated by a scale factor k then the coordinated of the dilated figure is: A'(ka,kb)

Here we have:  k=0.5

Hence, we get:

   A(4,2) → A'(0.5×4,0.5×2)=A'(2,1)

   B(2,4) → B'(2×0.5,4×0.5)=B'(1,2)

   C(6,4) → C'(6×0.5,4×0.5)=C'(3,2)

Hence, the coordinates of the transformed image is:

                     A'(2,1)

                     B'(1,2)

                     C'(3,2)

s

step-by-step explanation: