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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 + 1, and A = (7,1).

 Jun 8, 2024
 #1
avatar+129401 
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The slope of a perpendicular line  to y  = 3x + 1 through (7,1)  =  -1/3

The equation of this  line is   y = (-1/3)(x - 7) + 1  = (-1/3)x + 7/3 + 1   =  (-1/3)x + 10/3

 

To find the intersection point of these two lines

 

3x + 1 =   (-1/3)x + 10/3

 

3x + (1/3)x  = 10/3 -1

 

10/3 x = 7/3

 

10 x  = 7

 

x = 7/10 = .7

 

y = 3(7/10) + 1  =  31/10 = 3.1

 

The reflected point is   ( .7 - (7 - .7) , 3.1 - (1 - 3.1) )  = ( 1.4 (-5.6 , 5.2)

 

cool cool cool

 Jun 8, 2024

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