Assessments - 3, GPA: 4
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(4) Specify the dilation scale factor. (5) Tap [OK]. Transformation Using a Matrix or Vector (General Transform) General Transform lets you input a matrix and/or vector to transform a figure. The result of the transformation is drawn as a separate figure. For example, if you transform line segment AB, the line segment A’B’ will be drawn. You can perform the following types of transformations with General Transform. • Matrix Transformation: x-axis/y-axis symmetry, rotation, enlargement, reduction, etc. • Vector Transformation: Vertical and horizontal parallel displacement k General Transform Example In this example draw triangle ABC and then draw triangle A’B’C’, which is symmetrical to ABC about the x-axis. Next, we will draw triangle A’’B’’C’’ by performing a parallel displacement on triangle A’B’C’ of 1 unit along the x- and y-axis. 20050501 8-2-20 Drawing Figures 8-2-20 Drawing Figures Tip • All of the steps in the procedure below are performed using the Geometry application only. You can also use the Main application or eActivity application to perform matrix calculations and obtain the same transformation. You can drag a figure from Geometry to Main, which transforms values (matrix) and performs calculation, and drag the values (matrix) obtained as a result from Main to Geometry to draw the transformed figure. After performing the following procedure, see “Transform Example Using the Main Application” (page 8-2-22). If you need to, tap [Edit] and then [Clear All] before beginning this example. u ClassPad Operation (1) Tap q to turn on coordinate display in the Geometry window. •You can skip this step if you want, but turning on coordinate display helps you see how coordinates are changed by the transform operations. (2) Draw triangle ABC, and then select its three sides. (3) Tap [Draw], [Construct], and then [General Transform]. • This displays the Transform dialog box. (4) Since we want a triangle that is symmetrical about the x-axis to the original triangle, input [[1, 0], [0, –1]]. 20050501 8-2-21 Drawing Figures 8-2-21 Drawing Figures (5) Tap [OK]. • This draws triangle A’B’C’, which is symmetrical to triangle ABC about the x-axis. (6) Tap anywhere outside of the triangles to deselect the currently selected triangle. Next, select triangle A’B’C’. (7) Tap [Draw], [Construct], and then [General Transform]. (8) Now, to perform parallel displacement on triangle A’B’C’ by 1 unit along the x- and y-axis, input [1, 1]. 20050501 8-2-22 Drawing Figures 8-2-22 Drawing Figures (9) Tap [OK]. • This performs the parallel displacement and draws triangle A’’B’’C’’. Note • In the above example, we performed the transformation and the parallel displacement operations separately. You could also perform both operations at the same time, if you want. To do so, input both the matrix [[1, 0], [0, –1]] and the vector [1, 1] in step (4), and then tap [OK]. This will produce the result shown in step (9). k Transform Example Using the Main Application It might be easier to understand how General Transform works if you use the Main application (or eActivity application) in combination with the Geometry application. This makes it possible to perform the following types of operations. (a) In the Geometry application, you can select a point on the figure obtained using General Transform and the corresponding point on the original figure (for example, point A on the original figure and point A’ on the transformed figure), drag them to the Main application, and display the transformation expression in the Main application. (b) You can select a triangle in the Geometry application and drag it to the Main application to convert the triangle to a matrix (2-row . 3-column matrix that shows three vertices). Conversely, you can drag a 2-row . 3-column matrix input (or produced by a calculation) in the Main application to the Geometry application and draw the applicable triangle. Here we will show actual examples of (a) and (b). Tip • All of the above operations can also be performed using the eActivity application instead of the Main application. • For information about how to access the Geometry application from the Main application and about the different operations you can perform between them, see “2-9 Using the Main Application in Combination with Other Applications”. 20050501 8-2-23 Drawing Figures 8-2-23 Drawing Figures k (a) Operation Example The following procedure assumes that the results produced by the procedure under “General Transform Example” on page 8-2-19 are still on the Geometry application window. u ClassPad Operation (1) On the application menu, tap Jto start up the Main application. (2) Tap the down arrow button on the Main application toolbar. On the button list that appears, tap 3. • This opens the Geometry application and displays triangles ABC, A’B’C’, and A’’B’’C’’ on the Geometry window. (3) Select points A and A’. (4) While both points are selected, drag point A (or point A’) to the cursor position in the M...