Question

Which of the following shows the two lines of reflection that produce an equivalent transformation of the translation △STU→△S'T'U'?

Answer 1

the fourth one

Explanation:

The pre-image and image of the translation are given.

To find the lines of reflection, locate a midpoint M of the translation vector between any two corresponding points on the pre-image and image.

The figure shows two congruent triangles S T U and S prime T prime U prime.

Then find the midpoints of SM and MS'.

The figure shows the same triangles S T U and S prime T prime U prime as in the previous figure. Point K is a midpoint of segment M S. Point N is a midpoint of segment M S prime.

The lines of reflection are perpendicular to the vector and intersect with the vector at the second set of midpoints by the Theorem of composition of two reflections across two parallel lines.

The figure shows the same triangles S T U and S prime T prime U prime as in the previous figure. There are two lines. The first line passes through point K. The second line passes through point N. These lines are perpendicular to segment S, S prime.

Therefore, the correct graph is the fourth one.

Answer 2

The correct option is;

The fourth option

Please the attached drawing created with MS Visio

Explanation:

From the given figure, we have;

The orientation of ΔSTU is equal to the orientation of ΔS'T'U'

When the plane of reflection is assumed to be the y-axis, we have;

For a reflection about the y-axis, we have;

The coordinate of the preimage = (x, y)

The coordinate of the image after the reflection = (-x, y)

When the image (-x, y) is reflected again across the y-axis, and becomes the image, we have;

The coordinate of the preimage = (-x, y)

The coordinate of the image after the reflection = (x, y)

Therefore, a reflection twice across the same y-axis would result in an image having the same orientation as the preimage

Given that a y-axis is parallel to another y-axis, we have;

A reflection twice across two parallel axis would result in an image having the same orientation as the preimage

The correct option is the 4th option

Please see attached drawing created with MS Visio