Question

Identify the coordinates of the vertices of each figure after the similarity transformation.

Answer 1

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

• W(-4, 8)

• X(-4, 0)

• Y(-12, 4)

• Z(-8, 16)

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)