Question

42. Trapezoid HJKL undergoes a series of transformations to form trapezoid QPRS. 10 9 7 6 5 4 101 3 Di 1 2 3 4 5 6 7=B9O -10-7 -8 -7 -6 53 K! RI IS 2 -4 5 EG -7 10 If trapezoid HJKL can be mapped onto trapezoid QPRS, which sequence of transformations proves the two trapezoids are similar? A a dilation by a scale factor of 2 about the origin followed by a reflection across the x-axis B a dilation by a scale factor of 2 about the origin followed by a reflection across the y-axis a dilation by a scale factor of 2 about vertex K followed by a reflection across the x-axis с D a dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis​

Answer 1

The trapezoids are similar and can be proven through a dilation by a scale factor of 2 about vertex K followed by a reflection across the x-axis or the y-axis.

Step-by-step explanation:

In order to determine which sequence of transformations proves that trapezoids HJKL and QPRS are similar, we need to analyze the options given.

Option A, a dilation by a scale factor of 2 about the origin followed by a reflection across the x-axis, does not preserve the shape of the trapezoid and its proportions. Therefore, it is not a correct sequence of transformations.

Option B, a dilation by a scale factor of 2 about the origin followed by a reflection across the y-axis, also does not preserve the shape and proportions of the trapezoid. Hence, it is not correct either.

Option C, a dilation by a scale factor of 2 about vertex K followed by a reflection across the x-axis, does preserve the shape of the trapezoid. As such, this is a valid sequence of transformations.

Option D, a dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis, also preserves the shape of the trapezoid. Therefore, this is also a correct sequence of transformations.

Both options C and D result in similar trapezoids, so either one can be chosen as the correct answer.

Answer 2

The answer explains the transformations that could map one trapezoid onto another, showing that the shapes are similar trapezoids, but indicates that without specific positional information or a visual representation, the correct sequence of transformations cannot be determined from the given information.

Step-by-step explanation:

The question involves determining the sequence of transformations that maps trapezoid HJKL onto trapezoid QPRS, with the suggestion that a dilation followed by a reflection has been applied to achieve this mapping. To determine which sequence is correct, one must consider the properties of dilations and reflections. A dilation about a point scales all distances from that point by the same factor, while a reflection across an axis mirrors points across that axis. If the shapes can be mapped onto each other through such transformations, this implies that they are similar trapezoids.

Without the coordinates or a graph provided, we cannot give a definite answer to the specified transformation sequence in the question. However, if trapezoid HJKL is indeed similar to trapezoid QPRS, one could visualize and test the sequences:

• A dilation by a scale factor of 2 about the origin followed by a reflection across the x-axis.
• A dilation by a scale factor of 2 about the origin followed by a reflection across the y-axis.
• A dilation by a scale factor of 2 about vertex K followed by a reflection across the x-axis.
• A dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis.

To identify the correct sequence, one would need additional information such as the positions of the vertices or a visualization of the transformations.