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Let A = (6,2), and let B be the reflection of A over the line y = 2x + 5 . Find the coordinates of B.

 Jan 28, 2021
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A line  perpendicular to  the  given one has a slope of  -1/2

And the equation of this line through (6,2)  is

 

y= (-1/2) ( x - 6) + 2

y =(-1/2) x + 3 + 2

y =(-1/2) x + 5

 

 

To find the  x coordinate of the   intersection of these lines  :

 

2x + 5  = (-1/2x)  + 5

 

x  = 0  

 

y=  5

 

And  this is the  midpoint   of (6,2)  and its reflected point

 

To get from   (6,2)  to (0,5)   we  had to go  to the left 6  and up 3

 

Applying the same movement  from  (0,5)   we get the reflected point B  =  (  -6, 8)

 

 

cool cool cool

 Jan 29, 2021

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