Answer:
After translation:
Translation: (x, y) → (x-6, y-8)
W'X'Y'Z' = W'(-10, 0), X'(-10, -8), Y'(-18, -4), Z'(-14, 8)
After dilation:
Dilation: (x, y) → (2x, 2y), centered at (0, 0)
W''X''Y''Z'' = W'' (-20, 0), X'' (-8, 0) , Y'' (-24, 8), Z'' (-16, 32)
Explanation:
Given the vertices of the Quadrilateral WXYZ
As the rule of translation is given by
Translation: (x, y) → (x-6, y-8)
So, after the translation the vertices of Quadrilateral WXYZ will be translated as:
W(-4, 8) → (x-6, y-8) ⇒ (-4-6, 8-8) = W'(-10, 0)
X(-4, 0) → (x-6, y-8) ⇒ (-4-6, 0-8) = X'(-10, -8)
Y(-12, 4) → (x-6, y-8) ⇒ (-12-6, 4-8) = Y'(-18, -4)
Z(-8, 16) → (x-6, y-8) ⇒ (-8-6, 16-8) = Z'(-14, 8)
Therefore,
W'X'Y'Z' = W'(-10, 0), X'(-10, -8), Y'(-18, -4), Z'(-14, 8)
Next, the rule of dilation is given by
Dilation: (x, y) → (2x, 2y), centered at (0, 0)
W'(-10, 0) → (2x, 2y) ⇒ (2(-10), 2(0)) = W'' (-20, 0)
X'(-4, 0) → (2x, 2y) ⇒ (2(-4), 2(0)) = X'' (-8, 0)
Y'(-12, 4) → (2x, 2y) ⇒ (2(-12), 2(4)) = Y'' (-24, 8)
Z'(-8, 16) → (2x, 2y) ⇒ (2(-8), 2(16)) = Z'' (-16, 32)
Therefore,
W''X''Y''Z'' = W'' (-20, 0), X'' (-8, 0) , Y'' (-24, 8), Z'' (-16, 32)