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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 14: Q10. (page 580)

Write the coordinates of the image of each point by reflection in,
The $x - a x i s$
The $y - a x i s$
The line $y = x$ (Hint: Refer to the Example on page 578)
Point D.

Short Answer

Expert verified

$R_{x - a x i s} : D = (- 2, 1) \to (- 2, - 1)$
$R_{y - a x i s} : D = (- 2, 1) \to (2, 1)$
$R_{y = x} : D = (- 2, 1) \to (1, - 2)$

Step by step solution

01

a.Step 1. Given Information.

Coordinate of point D is $(- 2, 1)$

02

Step 2. Explanation.

Image of $(- 2, 1)$ in the x-axis is $(- 2, - 1)$

03

Step 3. Conclusion.

So, the image of D in the $x - a x i s$ is $R_{x - a x i s} : D = (- 2, 1) \to (- 2, - 1)$

04

b.Step 1. Given Information.

Coordinate of point D is $(- 2, 1)$

05

Step 2. Calculation.

Image of $(- 2, 1)$ in the y-axis is $(2, 1)$ .

06

Step 3. Conclusion.

So, $R_{y - a x i s} : D = (- 2, 1) \to (2, 1)$ .

07

c.Step 1. Given Information.

Coordinate of point D is $(- 2, 1)$

08

Step 2. Calculation.

Image of $(- 2, 1)$ in the line $x = y$ is $(1, - 2)$

09

Step 3. Conclusion.

Therefore, $R_{y = x} : D = (- 2, 1) \to (1, - 2)$ .

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Most popular questions from this chapter

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

$R_{j} (\underline{?}) = \vec{X Y}$

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 $\vec{O P}$ intersects the blue squares.

Is the mapping a one-to-one?
Copy the diagram and locate a point X that is its own image.
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 $R S \neq R' S'$ .
Does the mapping preserve distance?
Describe a mapping from the red square onto the blue square that does preserve distance.

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 $\vec{O P}$ to a point $P'$ of the cylinder.

Does the North Pole (pointN) have an image?

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

$R_{k} (C) = \underline{?}$

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

See all solutions

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