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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 $(x,y)$.

 

Point A is (5,7), and the line is y = x.

 Jan 15, 2024
 #1
avatar+36919 
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y = 1 (x) 

find perpendicular line 

y = -x 

that passes through the point (5,7) 

y = -x + 12 

Intersection point is 6,6     ( found by equating    y =  x   and   y = -x +12 ) 

(6,6) IS THE midpoint BETWEEN the original point (5,7) and the reflected point (x,y)  

    so      ( 5+x ) / 2 = 6    and    (7+y) / 2 = 6    shows  (x,y) to be    (7, 5) 

 

This is pretty easy to see with a line  y = x .....but this is the method to use for more diffiicult line equatins such as ' y = 5x '    etc......

 Jan 15, 2024

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