A transformation that maps the vertex A( 3 , 4 ) to A’ ( -4 , 3 ) is

"A translation of 7 units to the left followed by a translation of 1 unit down".

Step-by-step explanation:

There are multiple transformations that map one point into another, here is one example that works particularly for translations, which are the simplest (and usually the most used) transformations.

Suppose that we have the point (a, b) which is transformed into (a', b')

Then we have a horizontal translation of (a' - a) units followed by a vertical translation of (b' - b) units.

(the order of the translations does not matter, is the same having first the vertical translation and then the horizontal one).

Here we have the point A (3, 4) transformed into (-4, 3)

Then we have a horizontal translation of ((-4) - 3) = -7 units followed by a vertical translation of (3 - 4) = -1 units.

Where a horizontal translation of -7 units is a translation of 7 units to the left, and a vertical translation of -1 unit is a translation of 1 unit down.

Then we can write this transformation as:

"A translation of 7 units to the left followed by a translation of 1 unit down".

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