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Chapter 14: Q36. (page 582)

In each exercise Rk:A→A'. Find an equation of line k.

Short Answer

Expert verified

The equation is obtained as,

y=x+c

Step by step solution

01

Step 1. Given Information.

The given points are 0,2and4,6

02

Step 2. Concept Used.

y=mx+cwherem=y2−y1x2−x1

03

Step 3. Calculation.

The line of the given points can be obtained as,

m=y2−y1x2−x1m=6−24−0m=1y=1⋅x+cy=x+cwherecisconstant

04

Step 4. Conclusion.

Therefore, the equation is obtained as,

y=x+c

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Most popular questions from this chapter

Show that the light ray follows the shortest possible path from A and C via the mirror by proving that for any point E on the mirror (other than B) AE+EC>AB+BC. (Hint: See the Application: Finding the Shortest Path, on page 224.)

Draw a triangle and a line m such that Rm maps the triangle to itself. What kind of triangle did you use?

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.

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

Rk Stands for ?¯.

In each exercise Rk:A→A'. Find an equation of line k.
See all solutions

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