Chapter 12.4, Problem 20E

To determine

To describe: The translation from the image to the original figure using the given coordinate notation.

Answer to Problem 20E

The coordinate notation for translation from image to original figure will be as follows:

$(x,y)\to (x\text{'}+3,y\text{'}-5)$

Where $(x\text{'},y\text{'})$ are the coordinates of the image.

Explanation of Solution

Given information:

The following coordinate notation:

$(x,y)\to (x-3,y+5)$

To describe the translation from the image to the original figure, the coordinate notation is used. According to the coordinate notation, the image will move $3$ units to the left of the original figure and $5$ units up the original figure. Therefore, the image will be to the left and up the original figure. But here, the translation of the original figure from the image is to be described. Since the image is to the left and up the original figure, it is obvious that the original figure is to the right and down the image. Therefore, the original will be $3$ units to the right and $5$ units down the image. Consider $(x\text{'},y\text{'})$ to be the coordinates of the image, the coordinate notation for translation from image to original figure will be as follows:

$(x,y)\to (x\text{'}+3,y\text{'}-5)$