Multiple Transformations Lesson

Multiple Transformations Lesson

Pre-Algebra

Unit 5

Multiple Transformations

• Sometimes more than one transformation is applied to an image. When this happens, you will do one transformation and then a second one. Let's look at some examples.

Example 1: Reflect, Then Translate

Triangle TUV was reflected over the x- axis and then translated -2 horizontally. What are the new coordinates of the image?

We will apply the reflection first. Triangle TUV should be reflected over the x-axis, so the y-coordinates will become the opposite coordinate.

At this point, the new coordinates for TUV can be seen with green dots (T'(-4,4), U'(8,4), V'(8,-8)). Now we will take those new points and translate them down 2 because the problem says that we need to translate them -2 vertically.

After the image was translated down 2 (the orange arrows show that translation), we then connected the points to show the new image. We can look at what was done mathematically.

So, after a reflection over the x-axis and a translation -2 vertically, the new coordinates for triangle TUV are T'(-4,2), U'(8,2), and V'(8,-10).

Example 2: Translate, Then Reflect

Rectangle LMNO was translated 4 units down and 2 units right. Then, the new image was reflected over the y-axis. Sketch the image after the translation and reflection.

First, we will translate. 

After the translation, the new points for rectangle LMNO are L'(-4,-1), M'(-4,-3), N'(1,-3), and O'(1,-1). Once we have translated, we can now reflected those new points over the y-axis.

For this example, we needed to sketch the image, so you can see that in the problem above; however, we will go ahead and show how we were able to get the new coordinates mathematically as well.

• So, after a translation of -4 units vertically and -2 units horizontally and then a reflection over the y-axis, the new coordinates of rectangle LMNO are L'(4, -1), M'(4, -3), N'(-1, -3), and O'(-1, -1).

Multiple Choice

Plot A(4,1) B(5,4) C(1,2). Reflect it over the x-axis, then translate it 3 units left. What are the coordinates of A'B'C'?

• A' (-1, -1) B' (-2, -4) C' (2, -2)

• A' (4, -4) B' (5, -7) C' (1, -5)

• A' (-7, 1) B' (-8, 4) C' (-4, 2)

• A' (1, -1) B' (2, -4) C' (-2, -2)

Multiple Choice

Two trapezoids are shown on the coordinate grid. Which sequence of transformations shows that the two trapezoids are congruent

• Reflect Trapezoid 1 across the x-axis, then reflect the resulting figure across the y-axis.

• Translate Trapezoid 1 to the right 4 units, then reflect the resulting figure across the x-axis.

• Translate Trapezoid 1 to the right 4 units, then translate the resulting figure down 4 units.

• Translate Trapezoid 1 down 4 units, then reflect the resulting figure across the x-axis.

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformation shows that  $\Delta ABC\cong\Delta DEF$  ?

• Reflect △ABC across the x-axis, then translate it down 2

• Reflect △ABC across the y-axis, then translate it down 2

• Reflect △ABC across the x-axis, then translate it up 2

• Reflect △ABC across the y-axis, then translate it up 2

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that ΔABC≅ΔDEF

• Reflect △ABC across the x-axis, then translate it right 1

• Reflect △ABC across the y-axis, then translate it right 1

• Reflect △ABC across the x-axis, then translate it left 1

• Reflect △ABC across the y-axis, then translate it left 1

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that

 $\Delta ABC\cong\Delta DEF$  

• Reflect △ABC across the x-axis, then translate it down 1

• Reflect △ABC across the x-axis, then translate it up 1

• Reflect △ABC across the y-axis, then translate it down 1

• Reflect △ABC across the y-axis, then translate it up 1