Question

problem 4 is there a transformation or sequence of translations, rotations, reflections, or dilations that moves one figure onto the other? yes no describe how you know its not possible.

Explanation:

Step1: Analyze side - length ratios

The purple rectangle has a length of 3 units and a width of 2 units. The red rectangle has a length of 6 units and a width of 4 units. The ratio of the lengths is $\frac{6}{3}=2$ and the ratio of the widths is $\frac{4}{2}=2$. So, there is a dilation with a scale factor of 2.

Step2: Check for additional transformations

After dilation, we can translate the dilated purple - rectangle to match the position of the red rectangle. First, dilate the purple rectangle by a scale factor of 2 with respect to the origin (or any fixed point). Then, translate it horizontally and vertically to align with the red rectangle.

Answer:

Yes, there is a sequence of transformations (a dilation with a scale factor of 2 followed by a translation) that moves one figure onto the other.