Reflection over the line y=−x is a geometric transformation where each point of an object is mapped to a new position, with the line y=−x acting as a mirror.
The line connecting the original point to its image will be perpendicular to the line , and the distance from the original point to the mirror line is equal to the distance from its image to the mirror line.
If a line has the equation y=−4x−2 is reflected over the line y=−x, determine the equation of its image.
To find the equation of the image, we use the rule x′=−y and y′=−x. This means we replace every x in the original equation with −y and every y with −x.
Original equation:
y=−4x−2
Substitute x→−y and y→−x:
(−x)=−4(−y)−2
Simplify the equation for the image line:
−x=4y−2
−x+2=4y
y=−41x+42
y=−41x+21
So, the equation of the image of the line y=−4x−2 after reflection over y=−x is y=−41x+21.
Line y=−4x−2 and its Image over y=−x
Reflection of the line y=−4x−2 over the line y=−x.
