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Chapter 14: Q7. (page 579)

Complete the following. Assume points D, C, U, W, X, and Y are obtained by reflection in link k or j.

Rk:BC→→?¯

Short Answer

Expert verified

CB is Reflection of BC in the line k,

Step by step solution

01

Step 1. Given Information.

C is the reflection of B and the given diagram is,

02

Step 2. Explanation.

As C is a reflection of B then B is the reflection Of C.

Now, Using Theorem 14.2 which states that A reflection in a line is isometry.

03

Step 3. Conclusion.

Hence, a similar figure is obtained. Now drawing it we have

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Most popular questions from this chapter

Mapping M maps points A and B to the same image point. Explain why the mapping M does not preserve distance.

A rolling ball that does not have much spin will bounce off a wall so that the two angles that the path forms with the wall are congruent. Thus, to roll the ball from B off the wall shown and into hole H, you need to aim the ball so that ∠1≅∠2.

  1. Let H' be the image of H by reflection in the wall. BH'→ Intersects the wall at P. Why is ∠1≅∠3? Why is ∠3≅∠2? Why is ∠1≅∠2? You can conclude that if you aim for H', the ball will roll to H.
  2. Show that the distance travelled by the ball equals the distance H.

In Exercise 18-20, refer to the diagrams om page 578. Given the reflection Rm:PQ→→P'Q'→, write the key steps of a proof that PQ=P'Q' for each case.

Case 4.

Write the coordinates of the image of each point by reflection in,

  1. The x-axis
  2. The y-axis
  3. The line y=x (Hint: Refer to the Example on page 578)

Point C.

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 OP→to a point P'of the cylinder.

Describe the image of the globe’s equator.
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