ANSWER
[tex]( - \frac{3}{2} , - 1)[/tex]
EXPLANATION
From the graph, the coordinates of Y are:
[tex](3,2)[/tex]
We want to find the image of this point after a dilation by a scale factor of -½ about the origin.
The rule for the dilation is :
[tex](x,y)\to( - \frac{1}{2} x, - \frac{1}{2} y)[/tex]
To find the coordinates of Y', we plug the coordinates of Y.
[tex]Y(3,2)\to \: Y'( - \frac{1}{2} (3), - \frac{1}{2}(2) )[/tex]
[tex]Y(3,2)\to \: Y'( - \frac{3}{2}, - 1)[/tex]
The first choice is correct.
