Question

Which of the following transformations accurately describes the relationship between the two trapezoids?A. Dilate the blue trapezoid by a scale factor of ½ to obtain the red trapezoid.B. Dilate the red trapezoid by a scale factor of 2 to obtain the blue trapezoid.C. Dilate the red trapezoid by a scale factor of ½ to obtain the blue trapezoid.D. Dilate the blue trapezoid by a scale factor of 3 to obtain the red trapezoid.

Answer 1

Given: Two trapezoid as shown in the image

To Determine: The transformation that relates the two trapezoids

Solution

Let us determine the coordinates of the two trapezoid as shown below

We can relate the blue trapezoid to the red trapezoid

$\begin{gathered} (3,1.5)\rightarrow(6,3) \\ (4.5,1.5)\rightarrow(9,3) \\ (3,3)\rightarrow(6,6) \\ (4.5,4.5)\rightarrow(9,9) \end{gathered}$

It can be observed that the transformation rule that relates the blue trapezoid to the red trapezoid is

$(x,y)\rightarrow(2x,2y)$

It can be observed that the blue trapezoid is enlarged by a scale factor to get the red trapezoid. So, we dilate the blue trapzoid by a scale factor of 2 to get the red trapezoid.

From the options provided, the best answer related the red trapezoid to the blue trapezoid, which is a reduction by a scale factor of 1/2

Hence, the correct option is

Dilate the red trapezoid by a scale factor of 1/2 to obtain the blue trapezoid, OPTION C