Question

abcd and efch are quadrilaterals. given abcd - efgh, describe a sequence of rigid motions followed by a dilation with center (0,0) that maps abcd to efgh.
describe the sequence. select the correct choice below and fill in the answer boxes to complete your choice.
a. reflection across the y - axis, translation with center (0,0) and scale factor unit(s) left and unit(s) down, dilation
b. reflection across the x - axis, translation with center (0,0) and scale factor unit(s) left and unit(s) down, dilation
c. reflection across the x - axis, translation with center (0,0) and scale factor unit(s) right and unit(s) up, dilation

Explanation:

Step1: Analyze the position change

First, observe the relative position of the two quadrilaterals. We can see that quadrilateral \(ABCD\) needs to be reflected across the \(x -\)axis.

Step2: Analyze the translation

After reflection, we find that it needs to be translated \(1\) unit to the left and \(1\) unit down.

Step3: Analyze the dilation

Count the side - length ratio. Suppose the side - length of \(ABCD\) is \(2\) units and the side - length of \(EFGH\) is \(1\) unit. The scale factor of dilation with center \((0,0)\) is \(\frac{1}{2}\).

Answer:

B. Reflection across the \(x -\)axis, translation \(1\) unit left and \(1\) unit down, dilation with center \((0,0)\) and scale factor \(\frac{1}{2}\)