Question

Trapezoid K is the image of trapezoid K after a series of transformations.

Bella and Marco described the sequence of transformations in different ways.

Bella’s Sequence
Marco’s Sequence

1. a dilation of trapezoid K by a scale factor of mc021-3.jpg with the origin as the center of dilation
2. a rotation of mc021-4.jpg about the origin
3. a translation of 1 unit down

1. a reflection of trapezoid K across the x-axis
2. a dilation by a scale factor of mc021-5.jpg with the origin as the center of dilation
3. a translation of 1 unit down

Which sequence or sequences are correct and why?
Only Bella is correct.
Only Marco is correct.
Both Bella and Marco are correct because both chose the correct scale factor for the dilation and both describe other transformations that could be used.
Neither Bella nor Marco is correct because the scale factor they chose for the dilation is incorrect.

Answer 1

bella is correct, or a

Step-by-step explanation:

Answer 2

Bella's sequence is correct; For once, we can check the scale factor. The large side in the blue shape is 8 units long, while in the red shape it is 12. Hence, the scale factor is 12/8=1.5. Also, we have that the rotation part is correct, since the rotation needs to be 180 degrees to get an upside down version of the shape.
Marco's sequence is almost correct, but due to the reflection part, the 2 shapes should have the same orientation after this procedure. Hence, we get that the pointy parts of the shapes should point to the same direction. This is clearly not the case here, so Marco's procedure is wrong; in fact, his procedure yields almost the same object as the red one, only reflected along the y-axis.