Education Technology

Reflections over the Axes

Published on 06/09/2008

Activity Overview

It is important for students to know what happens to the coordinates of points when they are reflected over the x-axis or the y-axis. This activity enables students to use Cabri Jr. to develop this understanding.

Before the Activity

Prior to beginning this activity, students need to be familiar with how Cabri Jr. ? operates. Start the Cabri Jr. ? application with a new sketch.

During the Activity

Select the Hide/Show tool, option Axes, to display the coordinate axes. Select the Triangle tool to draw a triangle in the first quadrant. Select the Coord.&Eq. tool to display the coordinates for one of the vertices of the triangle. Select the Reflection tool. In order to reflect the triangle over the x-axis, select the triangle and then select the x-axis. Select the Coord.&Eq. tool to display the coordinates for the image of the vertex of the triangle that has coordinates already displayed. Grab the point of the preimage triangle that has coordinates displayed. Use it to move around the plane, noting the displayed coordinates as you do so. After exploring many situations, pose the question ?What do you notice about the coordinates of the preimage vertex and its image?? Restore the triangles to their positions before all the moves. Then, remove from view the image triangle, its vertices, and the displayed coordinates. Select the Reflection tool. Select the triangle to be reflected before selecting the y-axis. Select the Coord.&Eq. tool to display the coordinates for the image of the vertex of the triangle that has coordinates already displayed. Grab the point of the preimage triangle that has coordinates displayed. Use it to move around the plane, noting the displayed coordinates as you do so. After exploring many situations, pose the question ?What do you notice about the coordinates of the preimage vertex and its image??

After the Activity

After these investigations, students can summarize their findings. 1. If a point is reflected over the x-axis, its x-coordinate is unchanged, but its y-coordinate becomes its opposite. 2. If a point is reflected over the y-axis, its x-coordinate becomes its opposite, but its y-coordinate is unchanged. You may want to extend this conversation to talk about why preimage and image segments sometimes cross on the axes. Students can conjecture that it is because one of the coordinates is 0, and the opposite of 0 is still 0.