Published on 06/09/2008

#### Activity Overview

It is important for students to know what happens to the coordinates of points when they are rotated in the coordinate plane by 90 or 180 degrees, either clockwise or counterclockwise. 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. Also, students need to know that a positive angle measure causes a rotation in a counterclockwise direction. Similarly, a negative angle measure causes a rotation in a clockwise direction. Start the Cabri Jr. ? application with a new sketch.

#### During the Activity

Sselect the Hide/Show tool, option Axes, to display the coordinate axes. Select the Point tool, option Point, to place a point in the first quadrant. Select the Coord.&Eq. tool to display the coordinates of this point. It is helpful if the two coordinates are not equal. Sselect the Alph-Num tool to enter the number 90 in the upper-right hand corner of the screen. Sselect the Rotation tool. The order in which you select the elements of this transformation is very important. First, select the 90. Second, select the point about which the rotation will take place, in this case the origin. Third, select the point previously put in the first quadrant. This causes the image point to appear in the second quadrant. Select the Coord.&Eq. tool to display the coordinates for the image of the rotation. Grab the preimage point. 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 point and its image?? Restore the triangles to their positions before all the moves. Select the Alph-Num tool. Select the 90 and change it to 180. This produces a new image, which is the preimage point rotated 180?. Grab the preimage point. After exploring many situations, pose the question ?What do you notice about the coordinates of the preimage point and its image?? Restore the triangles to their positions before all the moves. Select the Alph-Num tool. Select the 180 and change it to -90. This produces a new image, which is the preimage point rotated -90?. Grab the preimage point. 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 point and its image??

#### After the Activity

After these investigations, students can summarize their findings. 1. If a point is rotated 90? counterclockwise, the x-coordinate of the preimage becomes the y-coordinate of the image, and the opposite of the y-coordinate of the preimage becomes the x-coordinate of the image. 2. If a point is rotated 180?, the opposite of x-coordinate of the preimage becomes the x-coordinate of the image, and the opposite of the y-coordinate of the preimage becomes the y-coordinate of the image. 3. If a point is rotated 90? clockwise, the opposite of the x-coordinate of the preimage becomes the y-coordinate of the image, and the y-coordinate of the preimage becomes the x-coordinate of the image.