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Section 7.2Reflections
OBJECTIVE:To find reflection images of figures
BIG IDEAS: Transformations and Coordinate GeometryESSENTIAL UNDERSTANDING:
• When you reflect a figure across a line, each point of the figure goes to another point the same distance from the
line, but on the other side.MATHEMATICAL PRACTICE:
Make sense of problems and persevere in solving them
A Reflection ( ) across a line m, called the line of reflection, is a transformation with the following properties:◦ If a point A is on line m, then the image of A is itself (that is )
◦ If a point B is not on line m, then m is the perpendicular bisector of
◦ When you reflect a figurethe shapes have oppositeorientations but are equidistantfrom the line.
Reflection across a Linemr
A A
BB
Reflections preserve ____________________
Reflections preserve _______________ measure
Reflections ____________ each point of the _______________ to one and only one corresponding point of its _______________
Reflections are _______________motions and _______________
Properties of Reflections
If and , then m mr A A r B B AB A B
If , then mr ABC A B C m ABC m A B C
a)
b)
c)
d)
e)
f)
EX 1: Find the coordinates of the image
1,4x axisr C
0,3y axisr D
2 4, 2yr E
1 3,5xr G
4,5y xr I
3, 1y axisr H
Reflections in the coordinate axes have the following properties:
◦ If is reflected in the x-axis, its image is the point
◦ If is reflected in the y-axis, its image is the point
◦ If is reflected in the line , its image is the point the same units above or below or left or right of the line, respectively
◦ If is reflected in the line , image is the point
Reflection Rules
,x y
,x y
,x y
,x y
,x y
,x y
,y x
or y b x a
y x
a) Graph points . Graph the coordinates of
EX 2: Find the coordinates of the image of the triangle
2, 1 , 2,2 , and 4, 3X Y Z x axisr XYZ
b) Graph points . Graph the coordinates of
EX 2: Find the coordinates of the image of the triangle
1,4 , 3,5 , and 2,1P Q R 2yr PQR
Math IXLL4 and L5
2 ribbons on L4 and Mastery on L5
