![]() ![]() If we were to fold the plane along the $x$-axis, the points A and A$^\prime$ match up with one another. Reflecting over the $x$-axis does not change the $x$-coordinate but changes the sign of the $y$-coordinate. Similarly the coordinates of $B$ are $(-4,-4)$ while $C = (4,-2)$ and $D = (2,1)$.īelow is a picture of the reflection of each of the four points over the $x$-axis: The coordinates of $A$ are $(-5,3)$ since $A$ is five units to the left of intersection of the axes and  3 units up. In order to help identify patterns in how the coordinates of the points change, the teacher may suggest for students to make a table of the points and their images after reflecting first over the $x$-axis and then over the $y$-axis: Point Thus the knowledge gained in this task will help students when they study transformations in the 8th grade and high school. Later students will learn that this combination of reflections represents a 180 degree rotation about the origin. This means that if we reflect over the $x$-axis and then the $y$-axis then both coordinates will change signs. Similarly when we reflect a point $(p,q)$ over the $y$-axis the $y$-coordinate stays the same but the $x$-coordinate changes signs so the image is $(-p,q)$.Â.When we reflect a point $(p,q)$ over the $x$-axis, the $x$-coordinate remains the same and the $y$- coordinate changes signs so the image is $(p,-q)$.The teacher may wish to prompt students to identify patterns in parts (b) and (c): Therefore, only (-2, 0) is the invariant point.The goal of this task is to give students practice plotting points and their reflections. Hence, the invariant points must have y-coordinate = 0. So, only those points are invariant which lie on the x-axis. We know that only those points which lie on the line are invariant points when reflected in the line. Prob-2: Which of the following points (-2, 0), (0, -5), (3, -3) are invariant points when reflected in the x-axis? We know that a point (x, y) maps onto (x, -y) when reflected in the x-axis. Prob-1: Find the points onto which the points (11, -8), (-6, -2) and (0, 4) are mapped when reflected in the x-axis. Solved examples to find the reflection of a point in the x-axis (v) The reflection of the point (-a, -b) in the x-axis = (-a, b) i.e., Mxx (-a, -b) = (-a, b) (iv) The reflection of the point (9, 0) in the x-axis is the point itself, therefore, the point (9, 0) is invariant with respect to x-axis. (i) The image of the point (3, 4) in the x-axis is the point (3, -4). Therefore, when a point is reflected in the x-axis, the sign of its ordinate changes. ![]() Change the sign of ordinate i.e., y-coordinate. ![]() Rules to find the reflection of a point in x-axis: The image of the point (x, y) in the x-axis is the point (x, -y). So, the y-coordinates of P’ will be – y while its x-coordinates will remain same as that of P. Let P be a point whose coordinates are (x, y).Ĭlearly, P’ will be similarly situated on that side of OX which is opposite to P. Reflection in the line y = 0 i.e., in the x-axis. If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located. When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). A reflection can be thought of as folding or “flipping” an object over the line of reflection.
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