Let (x1,y1) be the co-ordinate of new system, then x1=xcosθ+ysinθ y1=−xsinθ+ycosθ Given that (x1,y1)=(4,−3) and θ=135∘ 4=xcos135∘+ysin135∘ ⇒=−
x
√2
+
y
√2
−3=−xsin135∘+ycos135∘ . . . (i) −3=−
x
√2
−
y
√2
. . . (ii) On adding Eqs. (i) and (ii), we get 1=−