The coordinate of point T is (2,-4).
The perpendicular distance of point T from the line y=-x can be determined as,
[tex]\begin{gathered} p=\lvert\frac{2-4}{\sqrt[]{(2)^2+(4)^2}}\rvert \\ p=\frac{1}{\sqrt[]{5}} \end{gathered}[/tex]
The pependicular distance of point T' can be determined as,
[tex]p^{\prime}=\frac{a+b}{\sqrt[]{a^2+b^2}}[/tex]
As, T' is the reflection of T about line y+x=0 hence p=p',
[tex]\frac{a+b}{\sqrt[]{a^2+b^2}}=\frac{1}{\sqrt[]{5}}[/tex]
The only coordinate in quadrant IV which satisfies the above equation is (4,-2).
Thus, option (D) is correct.
