Point E with coordinates (5,7) is translated along a glide reflection to its image of E'(−7,9). Which best describes the glide reflection?
Answers
Given : Point E with coordinates (5,7) is translated along a glide reflection to its image of E'(−7,9).
To Find : glide reflection
Solution:
Let say line for glide reflection is
y = mx + c
E (5,7)
E'(−7,9)
Slope of line joining these
= (9 - 7)/(-7 - 5)
=2/(-12)
= -1/6
line for glide reflection will be perpendicular
Slope of line for glide reflection is is 6
y = 6x + c
E (5,7) E'(−7,9)
Mid point will lie on line for glide reflection
= (5 - 7)/2 , ( 7 + 9)/2
=( -1 , 8)
( -1 , 8) lies on y = 6x + c
=> 8 = 6(-1) + c
=> c = 14
=> y = 6x + 14
y = 6x + 14 is line for glide reflection
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