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Chapter 14: Q20. (page 580)

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

Case 4.

Short Answer

Expert verified

It is proved that, PQ=P'Q'.

Step by step solution

01

Step 1. Given Information.

It is given thatP'Q'炉is reflection of PQ in line m.

02

Step 2. Proof.

Since, P'Q'炉is reflection of PQin line m and it is visible in the figure that P and Q are not on the line m hence, m is perpendicular bisector of PP'andQQ'.

And if m is perpendicular bisector of both PP'andQQ'. Since, PP'andQQ'are not on same line then it obvious thatPP'andQQ'are parallel.

The two statements that m is perpendicular bisector of PP'andQQ',PP' is parallel toQQ'leads to conclude that PQ=P'Q'.

03

Step 3. Conclusion.

It is proved that, PQ=P'Q'.

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Most popular questions from this chapter

The transformation T:x,y鈫�x+y,y preserves areas of figures even though it does not preserve distances. Illustrate this by drawing a square with vertices A2,3,B4,3,C4,5, and D2,5, and its image A'B'C'D'. Find the area and perimeter of each figure.

Explain in your own words the meaning of each phrase.

  1. An isometry preserves distance.
  2. Area is invariant under a reflection.
  3. Orientation is not invariant under a reflection.

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

The red and blue squares are congruent and have the same center O. A mapping maps each point P of the red squares to the point P' where OP鈫� intersects the blue squares.

  1. Is the mapping a one-to-one?
  2. Copy the diagram and locate a point X that is its own image.
  3. Locate two points R and S on the red squares and their images R' and S' on the blue squares that have the property that RS鈮�R'S'.
  4. Does the mapping preserve distance?
  5. Describe a mapping from the red square onto the blue square that does preserve distance.

If function g:x鈫�8-3x, find the image of 5 and the pre image of 0.
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