Unit 1, Lesson 3
Making the Moves
Accelerated 7
3.1
Warm-up
Notice and Wonder: The Isometric Grid
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Your teacher will give you tracing paper to carry out the moves specified. Use
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
In Figure 2, translate triangle
In Figure 3, rotate triangle
In Figure 4, reflect triangle
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
In Figure 6, rotate quadrilateral
In Figure 7, reflect quadrilateral
In Figure 8, translate quadrilateral
Here are some figures on an isometric grid.
A transformation is a translation, rotation, reflection, or dilation, or a combination of these. An image is the result of a transformation. To distinguish an original figure from its image, points in the image are sometimes labeled with the same letters as the original figure, but with the symbol
A translation can be described by two points. If a translation moves point
For example, here is a translation of quadrilateral
A rotation can be described by an angle and a center. The direction of the angle can be clockwise or counterclockwise.
For example, hexagon
A reflection can be described by a line of reflection (the “mirror”). Each point is reflected directly across the line so that it is just as far from the mirror line, but is on the opposite side.
For example, pentagon
When we do one or more moves in a row, we often call that a sequence of transformations. For example, a sequence of transformations taking Triangle A to Triangle C is to translate Triangle A 4 units to the right, then reflect over line
There may be more than one way to describe or perform a transformation that results in the same image. For example, another sequence of transformations that would take Triangle A to Triangle C would be to reflect over line
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
A sequence of transformations is a set of translations, rotations, reflections, and dilations on a figure. The transformations are performed in a given order.
This diagram shows a sequence of transformations to move Figure A to Figure C.
First, A is translated to the right to make B. Next, B is reflected across line
A transformation is a translation, rotation, reflection, or dilation, or a combination of these.
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