Education Technology

Translations in the Coordinate Plane

Published on 06/09/2008

Activity Overview

It is important for students to know what happens to the coordinates of points when they are translated in the coordinate plane. 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. It may be helpful if the triangle is not special. Select the Point tool, option Point, to place a point above and to the right of the origin. Select the Coord.&Eq. tool to display the coordinates of one vertex of the triangle and for the single point placed in the drawing. In order to get the coordinates of the single point into a convenient place, make sure no tool is active, point to that point, depress the ALPHA key, and then move the coordinates to the lower left corner of the screen. Select the Translation tool. In order to determine the direction to translate the triangle, select the origin first and then the single point in the drawing. These points slowly blink. Then, select the triangle. The image of the triangle appears, showing where it finishes after moving parallel to the vector from the origin to the single point in the drawing. Select the Coord.&Eq. tool to display the coordinates of the image of the vertex of the triangle with displayed coordinates. Grab the single point in the drawing. Drag it around, noting the coordinates of the image as you do. 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. They may say it in different ways, but it will be something like this: If a preimage point with coordinates (x, y) is translated a units horizontally and b units vertically, the image point has coordinates (x + a, y + b).