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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
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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.
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
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)
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
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 )
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.
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)