Question

Julie said that the transformation rule that maps ABC - A’B’C’ can be given by (x, y) > (x + 3, y - 1). Describe Julie's error and give the correct transformation rule.

Answer 1

To correctly answer the question, let us verify that Julie's answer is incorrect.

Step 1: Identify the coordinates of the image and pre-image of any of the vertex.

Let us use the vertex C

The coordinates as shown in the diagram are:

`\begin{gathered} C(-1,\text{ 0)} \\ C^(\prime)(-4,\text{ 4)} \end{gathered}`

Step 2: Using the coordinate, calculate the transformation

The transformation as shown is a translation. Hence we can calculate the transformation by taking the difference of the coordinates:

`\begin{gathered} \text{Difference = (-4-(-1), 4 -0)} \\ \text{= (-3, 4)} \end{gathered}`

Step 3: State the rule:

The rule is thus:

`(x,\text{ y) }\to\text{ (x-3, y + 4)}`

Answer: Julie's error is a miscalculation of the steps in finding the transformation rule. The correct transformation rule is :

(x, y) -> (x-3, y + 4)