With a scale factor of 0.5 and the center of dilation at (0,0), what are the coordinates of the points of the image P' Q' R' S'?

in general if you have a point P that you are going to scale about a center of dilation (cx,cy) you end up with

$$P'=sf((P_x-c_x), (P_y-c_y))+(c_x,c_y)=$$

$$(sf(P_x-c_x)+c_x,~sf(P_y-c_y)+c_y)$$

here

$$c_x=c_y=0,~~sf=0.5$$

so we end up with

$$P'=(0.5 P_x, 0.5 P_y)$$

applying that to P=(2,2) we get

$$P'=(0.5\cdot 2, 0.5 \cdot 2)=(1,1)$$

you can figure out the rest of them

Thanks Rom,

I'd like to get back and have a proper look at this one!   

(Note that P=2,2; Q=6,4; R=6,8; S=2,8)

Hi Rom,

The wording of this question is not familiar to me, nor do i understand your answer, but, if a shape is being shrunk  by 50% about (0,0) isn't it just a matter of halving all the x values and halving all the y values hence getting

P'(1,1),  Q'(3,2)  R'(3,4)  S'(1,4)  ?

You are right Melody; but what if the centre of dilation was, say (2,3)?  In this case you would need to halve the difference between the Px-values and 2, and the difference between the Py-values and 3, and then add these halved differences back on to 2 and 3 respectively to get the P'x and P'y coordinates.  Rom gave the general procedure first, then started to apply it to the particular data set of the question. 

Thanks Alan, 

I just had some problems with Rom's notation but I get it now.