Segment ab is being dilated with the center at the origin. the image of a, point a" has coordinates of (3.2, 6.4). what is the scale factor of the dilation and the coordinates of point b"

the scale factor is 0.8 and the coordinates of point b" are (–3.2, –4.8).
the scale factor is 1.25 and the coordinates of point b" are (–3.2, –4.8).
the scale factor is 0.8 and the coordinates of point b"are (–5, –7.5).
the scale factor is 1.25 and the coordinates of point b" are (–5, –7.5).

 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

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

Thus, the correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:

the first option is the answer.