Question

the translation (x,y)(x+3,y-3) maps TUVW onto T'U'V'W. What translation maps T'U'V'W onto TUVW?
(x,y)(x+3,y-7)
(x,y)(x-7,y+3)
(x,y)(x+7,y-3)
(x,y)(x-3,y+7)

Answer 1

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 left and y-coordinates 3 units up.
This is expressed as (x - 3, y + 3).

Answer 2

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 https://brainly.com/question/1632445

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

3. A problem on range of the function  https://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.