Question

1. describe a sequence of transformations that could map the pre - image to the image.

1. which transformation does not preserve orientation?

1. which transformation does not preserve size?

1. what are the three transformations that produce congruent figures?

1. which transformation produces similar figures?

1. what is an example of a scale factor that would reduce a figure?

1. what is an example of scale factor that would enlarge a figure?

Explanation:

Question 3

Step1: Identify Translation Direction

First, observe the horizontal shift. The pre - image (original figure) and the image (transformed figure) can be shifted horizontally. Let's take a point, say \(A(-3,3)\) and \(A'(3,2)\). Wait, maybe a better approach: first, check the horizontal and vertical shifts. Alternatively, we can consider a translation and then a reflection or other transformations. Let's look at the coordinates:

Pre - image points: \(A(-3,3)\), \(B(-4,1)\), \(C(-2,-1)\), \(D(-2,2)\)

Image points: \(A'(3,2)\), \(B'(4,0)\), \(C'(2,-2)\), \(D'(2,1)\)

First, let's do a horizontal translation. The x - coordinate of \(A\) is \(-3\) and of \(A'\) is \(3\). The difference is \(3-(-3)=6\), so a horizontal translation of \(6\) units to the right. Then, the y - coordinate of \(A\) is \(3\) and of \(A'\) is \(2\), so a vertical translation of \(1\) unit down.

Alternatively, we can also consider a reflection, but the translation seems more straightforward.

So one possible sequence: Translate the pre - image 6 units to the right and 1 unit down.

(Another way: We can also check for reflection. If we reflect over the line \(x = 0\) (y - axis), the x - coordinates change sign. For point \(A(-3,3)\), reflection over y - axis gives \((3,3)\), then translate 1 unit down to get \((3,2)\) which is \(A'\). Let's check \(B(-4,1)\): reflection over y - axis is \((4,1)\), translate 1 unit down to \((4,0)\) which is \(B'\). \(C(-2,-1)\): reflection over y - axis is \((2,-1)\), translate 1 unit down to \((2,-2)\) which is \(C'\). \(D(-2,2)\): reflection over y - axis is \((2,2)\), translate 1 unit down to \((2,1)\) which is \(D'\). So another sequence: Reflect the pre - image over the y - axis and then translate 1 unit down.

Orientation in transformations: Rotation and translation preserve orientation (the order of points, clockwise or counter - clockwise, remains the same). Reflection (a flip over a line) changes the orientation. For example, if you have a triangle with vertices in clockwise order, after a reflection, the order becomes counter - clockwise (or vice - versa). Dilation preserves orientation (since it just scales the figure). So the transformation that does not preserve orientation is reflection.

Transformations: Translation, reflection, and rotation are rigid transformations (isometries) that preserve size (lengths, angles, area, etc.). Dilation is a transformation that changes the size of the figure. In dilation, we scale the figure by a scale factor \(k\). If \(k
eq1\), the size of the figure (e.g., side lengths, area) changes. So the transformation that does not preserve size is dilation.

Answer:

One possible sequence is: Reflect the pre - image over the y - axis and then translate 1 unit down (or translate 6 units to the right and 1 unit down, or other valid sequences of transformations like translation and then reflection etc.)

Question 4