Unit 1, Lesson 3
Making the Moves
Accelerated 7
3.1
Warm-up
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 , , , 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 .
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 attached, as in (pronounced “A prime”).
A translation can be described by two points. If a translation moves point to point , it moves the entire figure the same distance and direction as the distance and direction from to . The distance and direction of a translation can be shown by an arrow.
For example, here is a translation of quadrilateral that moves to .
A rotation can be described by an angle and a center. The direction of the angle can be clockwise or counterclockwise.
For example, hexagon is rotated counterclockwise using center .
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 is reflected across line .
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 , then translate Triangle A′ 4 units to the right.
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 .
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 to make C.
A transformation is a translation, rotation, reflection, or dilation, or a combination of these.