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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

If a transformation maps two parallel lines to two image lines that are also parallel, we say that parallelism is invariant under the transformation. Is parallelism invariant under a reflection?
  1. Plot the points A6,1,B3,4, and C1,-3 and their images A',B', and C' under the transformation R:x,y→-x,y.
  2. Prove that R is an isometry. (Hint: Let Px1,y1 and Qx2,y2 be any two points. Find P' and Q', and use the distance formula to show that PQ=P'Q'.)

For each transformation given:

  1. Plot the three points A0,4, B4,6, and C2,0, and their images A', B', and C' under the transformation.
  2. State whether the transformation appears to be an isometry.
  3. Find the pre image of 12,6.

D:x,y→3x,3y

Sketch each figure on the chalkboard. With a different color, sketch its image, using the dashed line as the line of reflection.

Prove that the point D which is as far behind the mirror as the object A is in front of the mirror lies on BC↔. (Hint: Show that ∠CBE and ∠EBD are supplementary.)
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