Reflection over x axis
(You should follow along and draw things out on a sheet of graph paper or on your computer, in order to make them clear.) Therefore, if you have a point at $(3, -5)$, it is three units to the right of the $y$-axis, but four units to the right of your axis of symmetry. The line $x = -1$ is a vertical line one unit to the left of the $y$-axis. Notice how each point of the original figure and its image are the same distance away from the line of reflection (which can be easily counted in this diagram since the line of reflection is vertical).Rather than think about transformation rules symbolically, and trying to generalize them, try thinking about them visually. Keep this idea in mind when working with lines of reflections that are neither the x-axis nor the y-axis. In other words, the line of reflection lies directly in the middle between the figure and its image - it is the perpendicular bisector of the segment joining any point to its image. P(x,y)→P'(-y,-x) or r y=-x(x,y) = (-y,-x)Įach point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. The reflection of the point (x, y) across the line y = -x is the point (-y, -x). The reflection of the point (x, y) across the line y = x is the point (y, x). When you reflect a point across the line y = -x, the x-coordinate and the y-coordinate change places and are negated (the signs are changed). When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places. Reflecting over the line y = x or y = -x: (the lines y = x or y = -x as the lines of reflection) The reflection of the point (x, y) across the y-axis is the point (-x, y).
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite. Reflecting over the y-axis: (the y-axis as the line of reflection) Such processes will allow you to see what is happening to the coordinates and help you remember the rule. Or you can measure how far your points are away from the line of reflection to locate your new image. Hint: If you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this example the x-axis) to see where your new figure will be located. The reflection of the point (x, y) across the x-axis is the point (x, -y). When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. Reflecting over the x-axis: (the x-axis as the line of reflection) If P in on the line, then it is its own reflection in line l. Part II (after the word “and”): The second part of the definition deals with point P being on line ?. The line ? will be the perpendicular bisector of the segment joining point P to point P’. The reflection of point P in this line will be point P’. Part I (up to the word “and”): Here we see line ? and point P not on line ?.
Order is reversed.)ĭefinition: A reflection is an isometry where if ? is any line and P is any point not on ?, then r ?(P) = P’ where ? is the perpendicular bisector of \(\overline \) and if P∈? then r ?(P) = P.