Question

quadrilaterals wxyz and wxyz are similar. identify the type of reflection performed and the scale factor. a) to obtain quadrilateral wxyz, quadrilateral wxyz is reflected across the x - axis and dilated with a scale factor of 1/2. b) to obtain quadrilateral wxyz, quadrilateral wxyz is reflected across the x - axis and dilated with a scale factor of 1/3. c) to obtain quadrilateral wxyz, quadrilateral wxyz is reflected across the x - axis and dilated with a scale factor of 2. d) to obtain quadrilateral wxyz, quadrilateral wxyz is reflected across the x - axis and dilated with a scale factor of 3.

Explanation:

Step1: Identify coordinates of WXYZ

Coordinates: $W(-6,8)$, $X(-2,8)$, $Y(-2,2)$, $Z(-6,2)$

Step2: Identify coordinates of W''X''Y''Z''

Coordinates: $W''(-4,-4)$, $X''(-2,-4)$, $Y''(-2,-1)$, $Z''(-4,-1)$

Step3: Verify x-axis reflection

Reflect WXYZ over x-axis: $(x,y)\to(x,-y)$
Result: $W'(-6,-8)$, $X'(-2,-8)$, $Y'(-2,-2)$, $Z'(-6,-2)$

Step4: Calculate scale factor

Compare $W'(-6,-8)$ to $W''(-4,-4)$:
Scale factor $k=\frac{-4}{-6}=\frac{1}{2}$ (matches all vertices)

Answer:

A) To obtain quadrilateral W''X''Y''Z'', quadrilateral WXYZ is reflected across the x-axis and dilated with a scale factor of 1/2.