In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction. In reflection, translation may also take place because of its changes in the position. Here, the original image is called pre-image, and its reflection is called image. The representation of pre-image and image are $ABC$ and $A’B’C’$ respectively. The reflection transformation may be in reference to the coordinate system $\text{(X-axis and Y-axis)}.$
While reflecting a point about the $x$-axis $(y = 0)$, the magnitude of its $y$-coordinate remains the same but its sign changes. But the $x$-coordinate remains the same. This is because we are taking it to the quadrant below it. So, we can say that ${\text{R}}_{x}(x,y) = (x,-y)$.
The image of $(x,y)$ under a reflection over the line $y = x$ is $(y,x).$
The image of $(x,y)$ under a reflection over the line $y = -x$ is $(-y,-x).$
Two lines are perpendicular or orthogonal if they meet at right angles.
For two perpendicular lines, all four angles formed by the two lines are equal to $90 ^ \circ$.
Two non-vertical lines are perpendicular if and only if the product of their slopes is $-1.$ In other words, the slopes of two perpendicular lines are negative reciprocals of each other. A vertical line has infinite slope and is perpendicular to only horizontal lines, which have slope zero.
So, the correct answer is $A;B;C;D.$
