Question

problem 23
what are the coordinates of u for the transformation (t⟨−3, 1⟩ ∘ d4) (△tuv) of t(−7, −6), u(−8, 3), and v(2, 1)?

Explanation:

Step1: Apply dilation \( D4 \) to \( U(-8, 3) \)

The dilation formula is \( (x, y) \to (4x, 4y) \).
For \( U(-8, 3) \), after dilation: \( (4\times(-8), 4\times3) = (-32, 12) \)

Step2: Apply translation \( T\langle -3, 1

angle \) to the dilated point
The translation formula is \( (x, y) \to (x - 3, y + 1) \).
For the point \( (-32, 12) \), after translation: \( (-32 - 3, 12 + 1) = (-35, 13) \)

Answer:

\( (-35, 13) \)