Answer:
a = -1, b = -2.5
Step-by-step explanation:
Rule for the dilation of a vector [tex]\binom{x}{y}[/tex] by a scale factor of k is,
(x, y) → (kx, ky)
BY using this rule for a vector [tex]\binom{-1}{4}[/tex] by a scale factor of 2.5
[tex]\binom{-1}{4}[/tex] → [tex]\binom{-2.5}{1}[/tex]
Followed by the rotation by 90° Or [tex]\frac{\pi }{2}[/tex] radians,
Rule for rotation of a vector by 90° is,
(x, y) → (-y, x)
By this rule vector [tex]\binom{-2.5}{1}[/tex] will become,
[tex]\binom{-2.5}{1}[/tex] → [tex]\binom{-1}{-2.5}[/tex]
If we represent this vector by [tex]\binom{a}{b}[/tex],
Then a = -1 and b = -2.5 will be the answer.
