4.1.1: Exercises

Math 104 Green · LibreTexts

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    Exercise \(\PageIndex{1}\)

    What type of movements are used to change the orientation and placement of a shape?

    Exercise \(\PageIndex{2}\)

    What is the name of the motion that renders a shape upside down?

    Exercise \(\PageIndex{3}\)

    What do we call the motion that moves a shape to the right or left or on the diagonal?

    Exercise \(\PageIndex{4}\)

    If you are going to tessellate the plane with a regular polygon, what is the sum of the interior angles that surround a vertex?

    Exercise \(\PageIndex{5}\)

    Does a regular heptagon tesselate the plane by itself?

    Exercise \(\PageIndex{6}\)

    What are the only regular polygons that will tessellate the plane by themselves?

    Exercise \(\PageIndex{7}\)

    What is the transformation called that revolves a shape about a point to a new position?

    Exercise \(\PageIndex{8}\)

    Transformational geometry is a study of what?

    Exercise \(\PageIndex{9}\)

    Describe how to achieve a rotation transformation.

    Exercise \(\PageIndex{10}\)

    Construct a \({90^ \circ }\) rotation of the triangle shown.

    A right triangle, A B C, and a point. The point is to the left of the triangle.

    Exercise \(\PageIndex{11}\)

    Shapes can be rotated around a point of rotation or a ____________.

    Exercise \(\PageIndex{12}\)

    What is the name of the transformation that involves a reflection and a translation?

    Exercise \(\PageIndex{13}\)

    What can a tessellation not have between shapes?

    Exercise \(\PageIndex{14}\)

    Describe the transformation shown.

    Two trapezoids are plotted on a rectangular grid. Each trapezoid can be described as follows. The top side measures 3.5. From its right, it goes 2 units bottom-right, then goes 4.5 units left, and then goes 2 units top-left. The first trapezoid is on the left-center of the grid. The second trapezoid is at the top-right of the grid. The first trapezoid is translated 5 units to the right and 5 units vertically.

    Exercise \(\PageIndex{15}\)

    What do we call a transformation that produces a mirror image?

    Exercise \(\PageIndex{16}\)

    Sketch the reflection of the shape about the dashed line.

    A shape and a dashed line.

    Exercise \(\PageIndex{17}\)

    Sketch the reflection of the shape about the dashed line.

    A shape and a dashed line. The line intersects the shape at two points. The line intersects the shapes at two points.

    Exercise \(\PageIndex{18}\)

    Sketch the translation of the shape 3 units to the right and 3 units vertically.

    An 11-sided polygon is plotted on a square grid.

    Exercise \(\PageIndex{19}\)

    Rotate the shape \({45^ \circ }\) about the rotation point using point \(A\) as your guide.

    A cylinder and a point. The bottom-right of the cylinder is marked A.

    Exercise \(\PageIndex{20}\)

    Do regular pentagons tessellate the plain by themselves?

    Exercise \(\PageIndex{21}\)

    What do regular tessellations have in common?

    Exercise \(\PageIndex{22}\)

    How would we name a tessellation of squares as shown in the figure?

    A square is made up of two rows of two smaller squares. A small circle is drawn at the center of the square where the four smaller squares meet.

    Exercise \(\PageIndex{23}\)

    How do we name a tessellation of octagons and squares as shown in the figure?

    A tessellation pattern is made up of four octagons. The octagons are joined such that it forms a square at the center. A circle is drawn partially overlapping two octagons and the square.

    Exercise \(\PageIndex{24}\)

    How would we name a tessellation of trapezoids as shown in the figure?

    A tessellation pattern is made up of two rows of four trapezoids, each. A circle is drawn at the center of the inner four trapezoids.

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