+1418 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).
+129771 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)
