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Let $B$ be the reflection of $A$ over the line $y = \frac{1}{5} x + 3$.  Find the coordinates of $B$ if $A = (1,4)$.

 Aug 19, 2023
 #1
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y=  (1/5)x + 3

A= ( 1, 4)

 

The slope of the  given line = (1/5)

 

Writing an equation  for a  perpendicular line with a  slope  of  -5 passing through (1,4)  we get

 

y = -5 ( x -1) + 4

y= -5x +9

 

Now, find the  x coordinate  of the  intersection of these  lines

(1/5)x + 3 = -5x + 9

(1/5)x + 3 = (-25/5)x + 9

(26/5)x = 6

x= 30/26 =  15/13

And  y = (1/5)(15/13) + 3 =  3/13 + 3 =  42/13 

 

So the intersection point is  (15/13, 42/13)

 

From (1, 4) To (15/13, 42/13)  we moved  (15/13 - 1)  = 2/13 on x   and  42/13 - 4   = -10/13 on y   

 

So...from the intersection point  of th e lines we need to make the  same  moves

 

So B=   (15/13 + 2/13 , 42/13 - 10/13)  =  ( 17/13, 32/13)

 

cool cool cool

 Aug 19, 2023

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