John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, ). what was his error?

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:

The image is given as:

The transformation rule is given as:

When the rule is applied on , we have:

Hence, John's claim is incorrect.

His error is that, he subtracted the points instead of adding them.

Read more about transformations at:

link

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