Rotation by angle θ in the positive direction ‌x′=x‌cos‌θ+ysin‌θ ‌y′=−xsin‌θ+y‌cos‌θ Let (x2,y2)=(−4√2,−2√2) Point before rotation ( x1,y1 ), x1‌=x2‌cos(−‌
Ï€
4
)+y2sin‌(−‌
Ï€
4
) ‌=x2(‌
√2
2
)−y2(‌
√2
2
) And y1=x2(‌
√2
2
)+y2(‌
√2
2
) ⇒‌‌x1‌=‌
√2
2
(−4√2)−‌
√2
2
(−2√2) ‌=−4+2=−2 ‌ And ‌y1‌=‌
√2
2
(−4√2)+‌
√2
2
(−2√2) ‌=−4−2=−6 So, point before rotation is (−2,−6) reflection about y=−x ⇒ Reflection of point (x,y) is (−y,−x) i.e., (6,2) Translation by +3 in X-axis ∴‌‌(α,β)=(6,−3,2) =(3,2) ∴‌‌α+β=3+2=5