Question

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?

Answer 1

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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