Question

11. Translate AABC A(3,6), B(4,2), C(5, 6) right 4 and up 3 units. Then reflect the triangle across the line x = 1. /1 a. What is the arrow rule to show the translation piece of the composition? 16 b. What are the vertices of the image after the composition? 19 c. Graph the original triangle and its images. x

Answer 1

We start by graphing the vertices of the triangle:

The first transformation is a translation 4 units to the right and 3 units up.

Then, we will get:

`\begin{gathered} A=(3,6)\longrightarrow A^(\prime)=(3+4,6+3)=(7,9) \\ B=(4,2)\longrightarrow B^(\prime)=(4+4,2+3)=(8,5) \\ C=(5,6)\longrightarrow C^(\prime)=(5+4,6+3)=(9,9) \end{gathered}`

The rule applied for this translation is:

`(x,y)\longrightarrow(x+4,y+3)`

Now we have to reflect the points across the vertical line x=1. Only the horizontal coordinates will change, while the vertical coordinates remain equal.

This transformation has the rule:

`(x,y)\longrightarrow(2-x,y)`

Then, we will have:

`\begin{gathered} A^(\prime)=(7,9)\longrightarrow A^(\prime)^(\prime)=(2-7,9)=(-5,9) \\ B^(\prime)=(8,5)\longrightarrow B^(\prime)^(\prime)=(2-8,5)=(-6,5) \\ C^(\prime)=(9,9)\longrightarrow C^(\prime)^(\prime)=(2-9,9)=(-7,9) \end{gathered}`

Now we can graph the image and the pre-image: