Answer: The correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation: Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).
We are to find the scale factor of the dilation and the co-ordinates of the point B''.
From the given graph, we note that
the co-ordinates of point A are (4, 8).
Now, If S is the scale factor of dilation, then we must have
[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]
So, the scale factor is 0.8.
Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be
[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]
Thus, the correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
