Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Reflecting Points in the Coordinate Plane, Lecture notes of Calculus

How to reflect points in the coordinate plane by using the same coordinate value for one axis and taking the opposite value for the other axis. It includes examples of reflecting points in the x-axis, y-axis, and both axes, as well as exercises for practice.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

amoda
amoda 🇺🇸

4.1

(13)

257 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
282 Chapter 6 Integers and the Coordinate Plane
You can refl ect a point in the x-axis, in the y-axis, or in both axes.
The red points are mirror images of each other
in the x-axis because the x-coordinates are the
same and the y-coordinates are opposites. So,
the red points are 3 units from the x-axis in
opposite directions. The red points represent
a refl ection in the x-axis.
The blue points are mirror images of each other
in the y-axis because the y-coordinates are the same and the x-coordinates
are opposites. So, the blue points are 4 units from the y-axis in opposite
directions. The blue points represent a refl ection in the y-axis.
EXAMPLE Refl ecting Points in One Axis
1
1
a. Refl ect (2, 4) in the x-axis.
Plot (2, 4).
To re fl ect (2, 4) in the x-axis, use
the same x-coordinate, 2, and take
the opposite of the y-coordinate.
The opposite of 4 is 4.
So, the refl ection of (2, 4) in
the x-axis is (2, 4).
b. Refl ect (3, 1) in the y-axis.
Plot (3, 1).
To re fl ect (3, 1) in the y-axis, use
the same y-coordinate, 1, and take
the opposite of the x-coordinate.
The opposite of 3 is 3.
So, the refl ection of (3, 1) in
the y-axis is (3, 1).
Lesson Tutorials
Refl ecting Points in the
Coordinate Plane
Extension
6.5
Refl ecting a Point in the Coordinate Plane
To re fl ect a point in the x-axis, use the same x-coordinate and take
the opposite of the y-coordinate.
To re fl ect a point in the y-axis, use the same y-coordinate and take
the opposite of the x-coordinate.
321Ź2Ź3Ź44
Ź3
Ź2
x
y
3
2
1
O
(Ź4, 1) (4, 1)
(1, 3)
(1, Ź3)
x
y
3
4
2
1
Ź3
Ź4
Ź2
4
321OŹ2Ź3Ź4
(Ź2, Ź4)
(Ź2, 4)
x
y
3
4
2
1
Ź3
Ź4
Ź2
4
321OŹ2Ź3Ź4
(Ź3, Ź1) (3, Ź1)
COMMON
CORE
Coordinate Plane
In this extension, you w ill
understand refl ections
of points in the
coordinate plane.
Learning Standard
6.NS.6b
pf2

Partial preview of the text

Download Reflecting Points in the Coordinate Plane and more Lecture notes Calculus in PDF only on Docsity!

282 Chapter 6 Integers and the Coordinate Plane

You can reflect a point in the x -axis, in the y -axis, or in both axes. The red points are mirror images of each other in the x -axis because the x -coordinates are the same and the y -coordinates are opposites. So, the red points are 3 units from the x -axis in opposite directions. The red points represent a reflection in the x-axis. The blue points are mirror images of each other in the y -axis because the y -coordinates are the same and the x -coordinates are opposites. So, the blue points are 4 units from the y -axis in opposite directions. The blue points represent a refl ection in the y-axis.

EXAMPLE 11 Reflecting Points in One Axis

a. Reflect (2, 4) in the x -axis. Plot (−2, 4). To refl ect (−2, 4) in the x -axis, use the same x -coordinate, −2, and take the opposite of the y -coordinate. The opposite of 4 is −4.

So, the reflection of (−2, 4) in the x -axis is (−2, −4). b. Reflect (3,1) in the y -axis. Plot (−3, −1). To refl ect (−3, −1) in the y -axis, use the same y -coordinate, −1, and take the opposite of the x -coordinate. The opposite of −3 is 3.

So, the reflection of (−3, −1) in the y -axis is (3, −1).

Lesson Tutorials

Reflecting Points in the

Coordinate Plane

Extension

Refl ecting a Point in the Coordinate Plane ● To refl ect a point in the x -axis, use the same x -coordinate and take the opposite of the y -coordinate. ● To refl ect a point in the y -axis, use the same y -coordinate and take the opposite of the x -coordinate.

Ź 4 Ź 3 Ź 2 1 2 3 4

Ź 3

Ź 2

x

y 3 2 1 O

(Ź4, 1) (4, 1)

(1, 3)

(1, Ź3)

x

y 3

4

2 1

Ź 3 Ź 4

Ź 2

Ź 4 Ź 3 Ź 2 O 1 2 3 4

(Ź2, Ź4)

(Ź2, 4)

x

y 3

4

2 1

Ź 3 Ź 4

Ź 2

Ź 4 Ź 3 Ź 2 O 1 2 3 4 (Ź3, Ź1) (3, Ź1)

COMMON

CORE

Coordinate Plane In this extension, you will ● (^) understand reflections of points in the coordinate plane. Learning Standard 6.NS.6b

Extension 6.5 Reflecting Points in the Coordinate Plane 283

EXAMPLE 22 Reflecting a Point in Both Axes

Refl ect (2, 1) in the x -axis followed by the y -axis.

Step1: First, plot (2, 1).

Step 2: Next, reflect (2, 1) in the x -axis. Use the same x -coordinate, 2, and take the opposite of the y -coordinate. The opposite of 1 is −1. The point (2, 1) reflected in the x -axis is (2, −1).

Step 3: Finally, reflect (2, −1) in the y -axis. Use the same y -coordinate, −1, and take the opposite of the x -coordinate. The opposite of 2 is −2. The point (2, −1) reflected in the y -axis is (−2, −1).

So, (2, 1) reflected in the x -axis followed by the y -axis is (−2, −1).

Refl ect the point in (a) the x -axis and (b) the y -axis.

1. (3, 2) 2. (−4, 4) 3. (−5, − 6 ) 4. (4, − 7 )

5. (0, − 1 ) 6. (−8, 0) 7. (2.5, 4.5) 8. ( − 5 —^1

2

Refl ect the point in the x -axis followed by the y -axis.

9. (4, 5) 10. (−1, 7) 11. (−2, − 2 ) 12. (6.5, −10.5) 13. REASONING A point is reflected in the x -axis. The reflected point is (3, − 9 ). What is the original point? What is the distance between the points? 14. REASONING A point is reflected in the y -axis. The reflected point is (5.75, 0). What is the original point? What is the distance between the points? 15. a. STRUCTURE In Exercises 9−12, reflect the point in the y -axis followed by the x -axis. Do you get the same results? Explain.

b. LOGIC Make a conjecture about how to use the coordinates of a point to find its reflection in both axes.

16. GEOMETRY The vertices of a triangle are (−1, 3), (−5, 3), and (−5, 7). How would you reflect the triangle in the x -axis? in the y -axis? Give the coordinates of the reflected triangle for each case.

When reflecting a second time, be sure to use the reflected point and not the original point.

Common Error Ź^4 Ź^3 Ź^21234

Ź 3

Ź 2

x

y 3 2 1 O

(2, 1)

(2, Ź1)

Ź 4 Ź 3 Ź 2 1 2 3 4

Ź 3

Ź 2

x

y 3 2 1 O

(2, 1)

(Ź2, Ź1) (2, Ź1)