Chapter 12.4, Problem 11E

To determine

To describe: The error in finding the coordinates of the endpoints of the image and correct it.

Answer to Problem 11E

The correct coordinates after translation will be:

$\begin{array}{l}\text{Original Image}\\ A(-4,-2)\to A\text{'}(-1,-6)\\ B(2,3)\to B\text{'}(5,-1)\end{array}$

Explanation of Solution

Given information:

The following coordinates:

$\begin{array}{l}\text{Original Image}\\ A(-4,-2)\to A\text{'}(-1,2)\\ B(2,3)\to B\text{'}(5,7)\end{array}$

The following coordinate notation:

$(x,y)\to (x+3,y-4)$

The coordinates of the image given is incorrect. To obtain the coordinates after translation, add or subtract the given units from $x$ and $y$ coordinates as mentioned in the coordinate notation for translation. Here, $3$ units are to be added to $x$ coordinate and $4$ units are to be subtracted from $y$ coordinate of each vertex. On adding and subtracting the given units, the following coordinates are obtained:

$\begin{array}{l}\text{Original Image}\\ (x,y)\to (x+3,y-4)\\ A(-4,-2)\to A\text{'}(-1,-6)\\ B(2,3)\to B\text{'}(5,-1)\end{array}$

On comparing the obtained coordinates of $A\text{'}(-1,-6)$ and $B\text{'}(5,-1)$ with the given coordinates of $A\text{'}(-1,2)$ and $B\text{'}(5,7)$ , it is observed that the coordinates of $x$ are same while the coordinates of $y$ are different. According to the coordinate notation, $4$ units are to be subtracted from $y$ , while in the given coordinates of $A\text{'}(-1,2)$ and $B\text{'}(5,7)$ , $4$ units are added to $y$ , which leads to incorrect results. Therefore, the correct results are obtained by adding $3$ units to $x$ and subtracting $4$ units from $y$ as done above.