Question

1.Using geometry vocabulary, describea sequence of transformation that maps p onto figure q.2. write transformation mapping rule for the sequence you describe in part (a)P:(-1,2) (-1,4) (-4,2)(-4,4)Q:(2,-2) (2,-5) (4,-2) (4,-5)

Answer 1

First, we transform the coordinates of the vertices of P 270° anticlockwise.

The 270° anticlockwise transformation rule, T, is defined as:

`T\colon(x,y)\to(y,-x)_{}`

Therefore,

`T(-1,2)=(2,1)`
`\begin{gathered} T(-1,4)=(4,1) \\ T(-4,2)=(2,4) \\ T(-4,4)=(4,4) \end{gathered}`

Let the resultant shape be named P'

Hence,

P': (2,1), (4,1) (2,4) (4,4)​

Next

We translate the resultant shape downwards by 6 units.

The transformation rule, S, for moving downwards by 6 units is given by:

`S\colon(x,y)\to(x,y-6)_{}`

Therefore,

`S(2,1)=(2,1-6)=(2,-5)`
`\begin{gathered} S(4,1)=(4,1-6)=(4,-5) \\ S(2,4)=(2,4-6)=(2,-2) \\ S(4,4)=(4,4-6)=(4,-2) \end{gathered}`

Hence, the image of S on P' is : (2,-2) (2,-5) (4,-2) (4,-5)​

This is illustrated by the image below