Unit 1, Lesson 12

Defining Translations

Geometry

Practice

Problem 1

Match each directed line segment with the translation from Polygon to Polygon by that directed line segment.

<p>Congruent polygons P and Q. Polygon Q is located horizontally to the right of Polygon Q. There is a gap between the polygons; they do not overlap.</p> — Translation 1

<p>Congruent polygons P and Q. Polygon Q is located horizontally to the right of Polygon P. The polygons overlap.</p> — Translation 2

<p>Congruent polygons P and Q. Polygon Q is located up and to the left of Polygon P.</p> — Translation 3

<p>Congruent polygons P and Q. Polygon Q is located down and to the right of Polygon P.</p> — Translation 4

Practice

Translation 1
Translation 2
Translation 3
Translation 4

Problem 2

Draw the image of quadrilateral when translated by the directed line segment . Label the image of as , the image of as , the image of as , and the image of as .

<p>Quadrilateral A B C D on an isometric grid. B is aligned vertically above D. Side C D is 2 units long. Directed line segment, v, points up and to the right, but more right than up.</p>

Problem 3

Which statement is true about a translation?

A translation takes a line to a parallel line or to itself.
A translation takes a line to a perpendicular line.
A translation requires a center of translation.
A translation requires a line of translation.

Problem 4

ForLesson 11: Defining Reflections

Select all the points that stay in the same location after being reflected across line .

<p>Line L, facing upward and to the right, goes through Points C and E. Points A, B and D sit to the left of the line.</p>

Problem 5

ForLesson 11: Defining Reflections

Lines and are perpendicular. A point has this property: Rotating 180 degrees using center has the same effect as reflecting over line .

<p>Perpendicular lines L and M, intersecting at point P. L is horizontal, m is vertical.</p>

Give two possible locations of .
Do all points in the plane have this property?

Problem 6

ForLesson 10: Rigid Transformations

There is a sequence of rigid transformations that takes to , to , and to . The same sequence takes to . Draw and label :

<p>Triangles A B C and A prime B prime C prime. Point D is located on side B C.</p>

Problem 7

ForLesson 6: Construction Techniques 4: Parallel and Perpendicular Lines

Two distinct lines and are each perpendicular to the same line .

What is the measure of the angle where line meets line ?
What is the measure of the angle where line meets line ?

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Defining Translations

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7