Question

triangle abc has vertices located at a(0,2) b(2,6) and c (4,2). triangle A’B’C’ is the result of dilating Triangle ABC using the origin as the center of dilation and a scale factor of 0.5. HELP

1. quangkhai
A’= (0, 1)
B’= (1, 3)
C’= (2, 1)
What is dilation of triangle?
The definition of a dilation is a transition in which the pre-image and the picture have the same shape but different sizes.
The image formed after the dilation is larger than the pre-image and is referred to as a “Enlargement” when the scale factor is more than 1.
The picture formed after the dilation is smaller than the pre-image and is referred to as a “Reduction” when the scale factor is between 0 and 1.
In this case you know that the triangle ABC was dilated by this scale factor: 0.5
With the origin as the center of dilation.
Since:
0< 0.5< 1
It is a Reduction.
The vertices of the triangle ABC are:
A(0,2), B(26) and C(4,2)
So you need to multiply the coordinates of each vertex  of the triangle ABC by 0.5, in order to get the coordinates of the triangle A’B’C. Then, you get:
A'(0(0.5), 2(0.5))= A'(0, 1)
B'(2(0.5), 6(0.5))= B'(1, 3)
C'(4(0.5), 2(0.5))= C'(2, 1)