91Ó°ÊÓ

Tell which of the following properties are invariant under the given transformation. a. distance b. angle measure c. area d. orientation The composite of two dilations

A piece of paper is wrapped around a globe of the Earth to form a cylinder as shown. \(O\) is the center of the Earth and a point \(P\) of the globe is projected along \(\overrightarrow{O P}\) to a point \(P^{\prime}\) of the cylinder. Is the image of the Arctic Circle congruent to the image of the equator?

Explain why a glide reflection is an isometry.

In Exercises \(21-23\) draw the figure if there is one that meets the conditions. Otherwise write not possible. A trapezoid with (a) no symmetry, (b) one symmetry line, (c) a symmetry point.

In Exercises \(21-23\) draw the figure if there is one that meets the conditions. Otherwise write not possible. An octagon with (a) eight rotational symmetries. (b) just four rotational (c) only point symmetry. symmetries,

A dilation with scale factor \(\frac{3}{4}\) maps a sphere with center \(C\) to a concentric sphere. a. What is the ratio of the surface areas of these spheres? b. What is the ratio of the volumes of these spheres?

A dilation with center \((a, b)\) and scale factor \(k\) maps \(A(3,4)\) to \(A^{\prime}(1,8)\) and \(B(3,2)\) to \(B^{\prime}(1,2) .\) Find the coordinates of the center \((a, b)\) and the value of \(k\).

A figure has \(50^{\circ}\) rotational symmetry. What other rotational symmetries must it have? Explain your answer.

Tell how many planes of symmetry and axes of rotation each solid has. a. a right circular cone b. a cube c. a regular tetrahedron (a pyramid formed by four equilateral triangles)