We are given transformation rule
(x, y) --> (x + 4, y + 7).
The coordinate of the pre-image is (4,5).
The coordinate of the transformed image is (0,-2).
Please see, if we apply
(x, y) --> (x + 4, y + 7) rule.
(4,5) coordinate would become (4 +4 , 5+7 ) = (8,12).
But we need (0,-2) instead of (8,12).
Let us reverse operation in the given rule and check.
Let us change (x + 4, y + 7) to (x-4, y-7) and now check.
(4,5) coordinate would become (4-4 , 5-7) = (0,-2).
So, we got exact coordinate of the transformed image.
Therefore, error was
(x, y) --> (x + 4, y + 7) rule should be (x, y) --> (x - 4, y - 7) rule.
Transformation involves changing the position of a point.
John's error is that, he subtracted the points instead of adding them.
The pre-image is given as:
[tex]\mathbf{(x,y) = (4,5)}[/tex]
The image is given as:
[tex]\mathbf{(x,y) = (0,-2)}[/tex]
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex]
When the rule [tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex] is applied on [tex]\mathbf{(x,y) = (4,5)}[/tex], we have:
[tex]\mathbf{(x,y) = (4+4,5+7)}[/tex]
[tex]\mathbf{(x,y) = (8,12)}[/tex]
Hence, John's claim is incorrect.
His error is that, he subtracted the points instead of adding them.
Read more about transformations at:
https://brainly.com/question/11709244
