Question

which transformations will produce similar, but not congruent, figures? select each correct answer. parallelogram jklm is dilated by a scale factor of 6 and then translated 2 units down to form parallelogram jklm. parallelogram jklm is translated 8 units left and then reflected across the x-axis to form parallelogram jklm. parallelogram jklm is rotated 90° clockwise and then reflected across the y-axis to form parallelogram jklm. parallelogram jklm is translated 6 units up and then dilated by a scale factor of 10 to form parallelogram jklm.

Explanation:

To determine which transformations produce similar but not congruent figures, we need to recall the properties of transformations:

• Congruent figures are produced by rigid transformations (translation, rotation, reflection) as they preserve size and shape.
• Similar figures have the same shape but not necessarily the same size. A dilation (scaling) changes the size, so if a dilation is involved (with a scale factor not equal to 1) along with other transformations, the figures will be similar but not congruent. Rigid transformations alone produce congruent figures.

Let's analyze each option:

Step 1: Analyze Option 1

• Transformation: Dilation (scale factor 6) then translation (2 units down).
• Dilation changes the size (scale factor 6 ≠ 1), so the resulting figure will have the same shape (similar) but different size (not congruent).

Step 2: Analyze Option 2

• Transformation: Translation (8 units left) then reflection (across x - axis).
• Both translation and reflection are rigid transformations. They preserve size and shape, so the figures will be congruent.

Step 3: Analyze Option 3

• Transformation: Rotation (90° clockwise) then reflection (across y - axis).
• Both rotation and reflection are rigid transformations. They preserve size and shape, so the figures will be congruent.

Step 4: Analyze Option 4

• Transformation: Translation (6 units up) then dilation (scale factor 10).
• Dilation (scale factor 10 ≠ 1) changes the size, so the resulting figure will have the same shape (similar) but different size (not congruent).

Answer:

• Parallelogram \( JKLM \) is dilated by a scale factor of 6 and then translated 2 units down to form parallelogram \( J''K''L''M'' \).
• Parallelogram \( JKLM \) is translated 6 units up and then dilated by a scale factor of 10 to form parallelogram \( J''K''L''M'' \).