Question

triangle A'B'C' is the image of triangle ABC under a reflection followed by a translation right 8 units and down 5 units.write the rules for the reflection and translation.

Answer 1

`\begin{gathered} Reflection\text{ Rule:}(x,y)\to(-x,y) \\ \text{Translation Rule:}(x,y)\to(x+8,y-5) \end{gathered}`

Explanation:

Consider the graph below:

In order to explain this, we use point A as a reference point.

• Point A on the pre-image is located at (3,6).

When A is reflected across the y-axis, its corresponding position is at (-3,6).

Thus, the rule for this reflection is:

`(x,y)\to(-x,y)`

Next, the reflection is followed by a translation right 8 units and down 5 units.

`(-3,6)\to(-3+8,6-5)=A^(\prime)(5,1)`

Therefore, the translation rule is:

`(x,y)\to(x+8,y-5)`