Question

Given the pre-image coordinates (0, 5), (-3, 2), (4, -1) and transformed image coordinates (2, -5), (-1, -2), (6, 1), what is the coordinate transformation in function notation?

Answer 1

Given:

The pre-image coordinates (0, 5), (-3, 2), (4, -1) and transformed image coordinates (2, -5), (-1, -2), (6, 1).

Required:

We need to find the transformation in function notation.

Step-by-step explanation:

Let (x,y) be the pre-image coordinate and (x',y') be the transformed image coordinates.

The transformation is

`(x,y)\rightarrow(x^(\prime),y^(\prime)).`

Consider the points (0,5) and (2,-5).

Substitute the values in the transformation.

`(0,5)\rightarrow(2,-5)`

`(0,5)\rightarrow(0+2,-(5))`

Let x =0 and y =5, we get

`(x,y)\rightarrow(x+2,-y)`

Consider the points (-3,2) and (-1,-2).

`(-3,2)\rightarrow(-1,-2)`
`Use\text{ }-3+2=-1.`

`(-3,2)\rightarrow(-3+2,-(2))`

Let x =-3 and y=2.

`(x,y)\rightarrow(x+2,-y)`

Consider the points (4,-1) and (6,-1).

`(4,-1)\rightarrow(6,1)`
`Use\text{ }4+2=6.`

`(4,-1)\rightarrow(4+1,-(1))`

`(x,y)\rightarrow(x+2,-y)`

`f(x,y)=(x+2,-y)`

Final answer:

`(x,y)\rightarrow(x+2,-y)`

`f:(x,y)\rightarrow(x+2,-y)`