Question

Which of the following transformations would make corresponding line
segments between a pre-image and image not be parallel?
Rotating 180° about a point not colinear with the segment.
Rotating 90° around a point not on the line segment.
Translating in a direction that is perpendicular to the line segment,
Reflecting over a line that is parallel to the line segment

Answer 1

A transformations that gives an image not parallel to the preimage, results in an image with points not equidistant from a common line.

Response:

• Rotating 90° around a point not on the line segment

How are the given transformations evaluated?

Required:

The transformation that will make the corresponding line segments

between a preimage and an image not parallel.

Solution:

The coordinate of a point (x, y) following a rotation of 180° is (-x, -y) Therefore, the distance from the x and y axis are maintained, forming a parallel image.

• The coordinate of a point (x, y) following a rotation of 90° is (y, -x) or (-y, x)

Therefore;

• The distance from the x and y-axis is reversed, and the image is not parallel to the preimage

The coordinate of a point (x, y) following a translation perpendicular to the line segment gives an image and preimage that are both perpendicular to the line of translation and therefore, parallel.

A reflection over a line parallel to the line segment gives an image that are equidistant from the line of reflection, as the corresponding points on the preimage, and therefore parallel to the preimage.

The correct option is therefore;

• Rotating 90° around a point not on the line segment

Learn more about rigid transformations here:

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