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qwelly [4]
3 years ago
12

The translation (x,y)(x+3,y-3) maps TUVW onto T'U'V'W. What translation maps T'U'V'W onto TUVW?

Mathematics
2 answers:
leva [86]3 years ago
8 0
Mapping T'U'V'W' onto TUVW is just the backwards translations of TUVW to T'U'V'W'.

The translation (x + 3, y - 3) moves all x-coordinates 3 units to the right and all y-coordinates 3 units down.

So if we want to move the figure back to its original position, we do the opposite: move all x-coordinates 3 units to the <em>left</em> and y-coordinates 3 units <em>up</em>.
This is expressed as (x - 3, y + 3).
Veronika [31]3 years ago
6 0

The translation of the mapping T'U'V'W' onto TUVW is \boxed{(x,y)\rightarrow(x-3,y+3)}.

Further explanation:

A transformation T:X\rightarrow Y is onto if any element of Y gives some element in X as the pre image of the translation in Y.

Given:

The given translation (x,y)\rightarrow(x+3,y-3)maps TUVW onto T'U'V'W'.

Calculation:

The mapping T'U'V'W' onto TUVW is the backward translation of the mapping TUVW onto T'U'V'W'.

In the given translation (x,y)\rightarrow (x+3,y-3) the coordinates of the x-axis move by 3 units in the right direction and the coordinates of the y-axis move by 3 units in the downward direction.

So, for the mapping T'U'V'W' onto TUVW we have to move back to the original position.

The following steps are involved to reverse the mapping.

1) As earlier discussed the all x-coordinate move by 3 units in the right direction so the opposite of this is move all x-coordinate by 3 units in the left direction. Therefore, the translation for the x-axis would be x-3.

2) As earlier the all y-coordinate move by 3 units in the downward direction so the opposite of this is move all y-coordinate by 3 units in the upward direction. Therefore, the translation for the x-axis would be y+3.

Thus, the translation of the mapping T'U'V'W' onto TUVW is \boxed{(x,y)\rightarrow (x-3,y+3)}.

Learn more:

1. A problem on inverse function brainly.com/question/1632445

2. A problem on domain and the range of the function brainly.com/question/3412497

3. A problem on range of the function  brainly.com/question/1435353

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords:  Onto mapping, one-one mapping, function, translation, x coordinate, y coordinate, coordinate, element, range , preimage, range, codomain, element, left direction, right direction, downward direction.

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