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Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = 3x - 2, and A = (-5,6).

 Jun 25, 2024
 #1
avatar+129725 
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A line through (-5.6)  perpendicular to the given  equation has the equation

 

y = -(1/3) (x + 5) + 6  →  -(1/3)x + 13/3

 

Set this equal to the given equation  to find the x intersection of these lines

 

3x - 2 = -(1/3)x + 13/3

(10/3)x = 19/3

x = 1.9

y = 3(1.9) - 2 = 3.7

 

The reflected point B  is

 

( 1.9 + (1.9 -  - 5) , 3.7 + (3.7 - 6) =  (1.9 + 6.9 , 3.7 - 2.3)  = (8.8 , 1.4)

 

cool cool cool

 Jun 25, 2024

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