This tutorial introduces you to reflections and shows you some examples of reflections. In math, you can create mirror images of figures by reflecting them over a given line. This will involve changing the coordinates.įor example, try to reflect over the -axis. y-axis Background Tutorials Transformations in the Coordinate Plane What is a Reflection When you look in the mirror, you see your reflection. In this lesson, we’ll go over reflections on a coordinate system. Reflection in the line x 0 i.e., in the y-axis. When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). The reflections of a function are transformations that make the graph of a function reflected over one of the axes. The objects appear as if they are mirror reflections, with right and left reversed. Do the same for the other points and the points are also Reflecting a function over the x-axis and y-axis.

On the same diagram, draw the image of the triangle ABC under reflection in the origin O. On a graph paper, plot the triangle ABC, whose vertices are at points A (3, 1), B (5, 0) and C (7, 4). Count two units below the x-axis and there is point A’. Reflection in y-axis is given by MY (x, y) (-x, y) Q’ Reflection of Q (5, 4) in y-axis (-5, 4) Hence, the co-ordinates of points P’ and Q’ are (-2, -3) and (-5, 4) respectively.

As a result, points of the image are going to be:īy counting the units, we know that point A is located two units above the x-axis. Since the reflection applied is going to be over the x-axis, that means negating the y-value. Determine the coordinate points of the image after a reflection over the x-axis. Triangle ABC with coordinate points A(1,2), B(3,5), and C(7,1). To get a reflection over the y-axis, we have to apply the transformation latex g(x)f(-x). You can also negate the value depending on the line of reflection where the x-value is negated if the reflection is over the y-axis and the y-value is negated if the reflection is over the x-axis.Įither way, the answer is the same thing.

To match the distance, you can count the number of units to the axis and plot a point on the corresponding point over the axis. Reflection over the y-axis A reflection in the y-axis can be seen in diagram 4, in which A is reflected to its image A. To reflect a shape over an axis, you can either match the distance of a point to the axis on the other side of using the reflection notation.

Reflection in y axis