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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: Q9. (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 C.

Short Answer

Expert verified

$R_{x - a x i s} : C = (0, - 2) \to (0, 2)$
$R_{y - a x i s} : C = (0, - 2) \to (0, - 2)$
$R_{y = x} : C = (0, - 2) \to (- 2, 0)$

Step by step solution

01

a.Step 1. Given Information.

Coordinate of point C is $(0, - 2)$ .

02

Step 2. Explanation.

Image of $(0, - 2)$ in the x-axis is $(0, 2)$ .

03

Step 3. Conclusion.

So, the image of C in the $x - a x i s$ is $R_{x - a x i s} : C = (0, - 2) \to (0, 2)$

04

b.Step 1. Given Information.

Coordinate of point C is $(0, - 2)$ .

05

Step 2. Calculation.

Image of $(0, - 2)$ in the y-axis is $(0, - 2)$ as the point is on y-axis

06

Step 3. Conclusion.

So, $R_{y - a x i s} : C = (0, - 2) \to (0, - 2)$ .

07

c.Step 1. Given Information.

Coordinate of point C is $(0, - 2)$ .

08

Step 2. Calculation.

Image of $(0, - 2)$ in the line $x = y$ is $(- 2, 0)$

09

Step 3. Conclusion.

Therefore, $R_{y = x} : C = (0, - 2) \to (- 2, 0)$ .

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Most popular questions from this chapter

$▵ X Y Z$ is isosceles with $\bar{X Y} ≅ \bar{X Z}$ . Describe a way of mapping each point of $\bar{X Y}$ to a point of $\bar{X Z}$ so that the mapping is an isometry.

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?

Explain how Corollary 2 follows from Theorem 14-1.

If function $g : x \to 8 - 3 x$ , find the image of 5 and the pre image of 0.

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

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