Which sequence of transformations produces an image that is not congruent to the original figure?A.A translation of 5 units to the left followed by a dilation of a factor of 2B.A reflection across the y-axis followed by a rotation of 180 counterclockwiseC.A translation of 3 units to the left followed by a reflection across the x-axisD.A rotation of 90 clockwise followed by a translation of 6 units to the leftSUBMITarrow_backPREVIOUS
Question
Which sequence of transformations produces an image that is not congruent to the original figure?A.A translation of 5 units to the left followed by a dilation of a factor of 2B.A reflection across the y-axis followed by a rotation of 180 counterclockwiseC.A translation of 3 units to the left followed by a reflection across the x-axisD.A rotation of 90 clockwise followed by a translation of 6 units to the leftSUBMITarrow_backPREVIOUS
Solution
The sequence of transformations that produces an image that is not congruent to the original figure is A. A translation of 5 units to the left followed by a dilation of a factor of 2.
This is because a dilation changes the size of the figure, not just its position or orientation. In other words, it alters the lengths of sides and the measures of angles, which means the figure is not congruent to the original. The other options (B, C, and D) involve only translations, reflections, and rotations, all of which are rigid transformations that do not change the size or shape of the figure, only its position or orientation. Therefore, they would produce an image that is congruent to the original figure.
Similar Questions
Tavon used a graphing program to graph a circle centered at the origin with a radius of 3 in the coordinate plane. He then applied two transformations to the original circle; first a dilation and then a translation. The new circle has a radius of 6 centered at the point (−1,0). Which of the following statements best explains the relationship between the original circle and its image under the sequence of transformations?ResponsesThe circle and its image are congruent because the sequence of transformations included a dilation with a scale factor of 2.Answer A: The circle and its image are congruent because the sequence of transformations included a dilation with a scale factor of 2 .AThe circle and its image are congruent because the sequence of transformations included a horizontal translation of 1 unit to the left.Answer B: The circle and its image are congruent because the sequence of transformations included a horizontal translation of 1 unit to the left.BThe circle and its image are similar but not congruent because the sequence of transformations included a dilation with a scale factor of 2.Answer C: The circle and its image are similar but not congruent because the sequence of transformations included a dilation with a scale factor of 2 .CThe circle and its image are similar but not congruent because the sequence of transformations included a horizontal translation of 1 unit to the left.
Which sequence of transformations will result in an image that maps onto itself?A.Rotate 180 degrees counterclockwise about the origin, and then reflect across the x-axis.B.Reflect over the y-axis, and then reflect again over the y-axis.C.Rotate 180 degrees counterclockwise about the origin, and then reflect across the y-axis.D.Reflect over the y-axis, and then reflect over the x-axis.
Which of the following are congruence transformations? Check all that apply.A.ReflectingB.StretchingC.ShrinkingD.RotatingE.TranslatingSUBMITarrow_backPREVIOUS
Which of the following transformations does not result in a congruent figure?
Which type of transformation is a mirror image of the original image? Write translation, rotation, reflection, or dilation in the space provided.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.