+0  
 
-1
14
1
avatar+1222 

Let $B$ be the reflection of $A$ over the line $y = \frac{1}{2} x + 2$.  Find the coordinates of $B$ if $A = (5,-1)$.

 Dec 20, 2023
 #1
avatar+129657 
+1

y = (1/2)x + 2

 

A line through  (5, -1)  that is  perpendicular  to  the  given line  has the equation

 

y = -2(x - 5) -1

y = -2x + 9

 

The x intersection of these two lines is

 

(1/2)x + 2 = -2x + 9

(5/2)x = 7

x = 14/5 =   2.8

 

And the y value is   -2(14/5) +9  =  17/5 = 3.4

 

From (5 , -1)   we move     [ (2.8-5) , (3.4 - - 1)  ]  =  [ -2.2 , 4.4] to the intersection point

 

So B =  [ 2.8 - 2.2 , 3.4 + 4.4]  =  (.6 , 7.8 ) 

 

 

cool cool cool

 Dec 20, 2023

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