Question

Please help and fast I don't understand

Answer 1

Problem 31:
The dilation factor is the distance of P'O (P' from origin) divided by PO.
To simplify matters, we only need the ratio of the x- or y-coordinates of P'O divided by that of PO.

We are given P'(6,4), and from the graph, we read P(9,6)
The dilation factor is therefore 6/9=2/3 (ratio of x-coordinates) or 4/6=2/3 (ratio of y-coordinates.


Problem 32:
Again, when the dilation is about the origin, we only need to know the ratio of x- or y-coordinates of C' divided by that of C.  C was chosen because both x and y coordinates of B and B' are integers, and also a longer distance CO and C'O can reduce interpretation errors.

Here, C'(15,9) and C(10,6)
So the dilation scale factor is 15/10=3/2, 
which means
(x,y) -> (3x/2, 3y/2)