Your teacher will give you tracing paper to carry out the moves specified. Use , , , and to indicate vertices in the new figure that correspond to the points , , , and in the original figure.
Four triangle A B C figures on a grid. Let (0 comma 0) be the bottom left corner of each figure. Figure 1 has point A prime at (7 comma 5) and the coordinates of triangle A B C are: (1 comma 3), B(3 comma 2) and C(5 comma 4). Figure 2 has point C prime at (7 comma 5) and the coordinates of triangle A B C are: (1 comma 3), B(3 comma 2) and C(5 comma 4). Figure 3 has point O at (6 comma 6) and the coordinates of triangle A B C are: (1 comma 4), B(3 comma 3) and C(5 comma 5). Figure 4 has line l at x = 6 and the coordinates of triangle A B C are: (1 comma 5), B(3 comma 4) and C(5 comma 6).
In Figure 1, translate triangle so that goes to .
In Figure 2, translate triangle so that goes to .
In Figure 3, rotate triangle counterclockwise using center .
In Figure 4, reflect triangle using line .
Four identical quadrilateral A B C D figures on a triangular grid. Figures are labeled Figure 5, Figure 6, Figure 7 and Figure 8. Each figure is in the upper left half of the figure box. Figure 7 has dashed line l parallel to the D C side across the figure box.
In Figure 5, rotate quadrilateral counterclockwise using center .
In Figure 6, rotate quadrilateral clockwise using center .
In Figure 7, reflect quadrilateral using line .
In Figure 8, translate quadrilateral so that goes to .
Student Lesson Summary
When a figure is on a grid, we can use the grid to describe a move. For example, here is a figure and an image of the figure after a move.
Two identical quadrilaterals on a grid labeled B D C A and B prime D prime C prime A prime. In quadrilateral B D C A, point B is 3 units right and 3 units down from the edge of the grid. Point D is 1 unit left and 1 unit up from point B. Point C is 2 units up from point B. Point A is 2 units right from point B. In quadritaleral B prime D prime C prime A prime, point B prime is 3 units down and 4 units right from point B. Point D prime is 3 units down and 4 units right from point D. Point C prime is 3 units down and 4 units right from point C. Point A prime is 3 units down and 4 units right from point A.
Quadrilateral is translated 4 units to the right and 3 units down to the position of quadrilateral .
This type of grid is called an isometric grid. The isometric grid is made up of equilateral triangles. The angles in the triangles all measure , making the isometric grid convenient for showing rotations of .
Here is quadrilateral and its image after a 60-degree counterclockwise rotation around a point .
Glossary
image
An image is the result of translations, rotations, and reflections on an object. Every part of the original object moves in the same way to match up with a part of the image.
Triangle has been translated up and to the right to make triangle . Triangle is the image of the original triangle .