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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 = x + 3, and A = (7,1).

 Jun 18, 2024
 #1
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Slope of the given line  = 1

 

Slope of the perpendicular line through A  = -1

Equation of this  line

y = -1 (x -7) + 1

y = -x + 8

 

x coordinate of the intersection of these lines

 

x + 3 = -x + 8

2x= 5

x  = 5/2  = 2.5

y = (2.5) + 3 =  5.5

 

B  = ( 2.5 + (2.5 - 7)  ,  5.5 + (5.5 -  1) )  =  (-2 , 10)

 

cool cool cool

 Jun 18, 2024

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