Question

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’

Answer 1

A= (2,1)
B=(1,2)
C=(3,2)

Answer 2

The coordinates of A’B’C’ are:

A'(2,1)

B'(1,2)

C'(3,2)

Explanation:

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)