Answer:
The fourth option:
J(7, - 15)
K ( -21, 62)
W(14, 32)
Explanation:
The counterclockwise rotation by 180 degrees about the origin corresponds to the following transformation of coordinates.
[tex](x,y)\to(-x,-y)[/tex]
This means that if we have the point J (-7, 15), then under 180 counterclockwise rotation about the origin, it transforms to
[tex]\begin{gathered} J(-7,15)\to J(--7,1-5) \\ \to J(7,-15) \end{gathered}[/tex]
Similarly, the point K(21, -62) transforms to
[tex]K\mleft(21,-62\mright)\to K(-21,62)[/tex]
and
[tex]W(-14,-32)\to W(14,32)[/tex]
Hence, to summerise, a 180-degree counterclockwise rotation about the origin brings about the following changes
[tex]\begin{gathered} J\mleft(7,-15\mright) \\ K(-21,62) \\ W\mleft(14,32\mright) \end{gathered}[/tex]