In the question, we are tasked to determine the coordinates of K after being dilated with a scale factor of 2/3.
Given Point K: (-6,-15)
To be able to dilate the point, we multiply the x and y coordinates by the given scale factor.
We get,
[tex]\text{ Point K: (-6,-15) }\rightarrow\text{ Point K': (-6)(2/3), (-15)(2/3)}[/tex][tex]\text{ Point K': (-12/3),(-30,3)}[/tex][tex]\text{ Point K': -4,-10}[/tex]
Therefore, the coordinates of point K' is (-4,-10).
The answer is letter B.
