Chapter 4, Problem 19SGR

To determine

To find: The coordinates of the image after translation $2$ units left and $3$ units up.

Answer to Problem 19SGR

The coordinates of the image of the triangle are $A^{\prime }\left(3,7\right)$ , $B^{\prime }\left(1,1\right)$ and $C^{\prime }\left(-3,4\right)$ .

Explanation of Solution

Given:

The given image f the triangle is as:

  

In order to find the coordinates of the image of the triangle, first, subtract $2$ from the $x$ co-ordinates and add $3$ to the $y$ coordinates in the A, B, C coordinates:

The image after transformation is given as:

  

The coordinates of the image of the triangle are calculated by using above graph is given as:

  $A^{\prime }\left(3,7\right)$ , $B^{\prime }\left(1,1\right)$ and $C^{\prime }\left(-3,4\right)$ .

Therefore, the coordinates of the image of the triangle are $A^{\prime }\left(3,7\right)$ , $B^{\prime }\left(1,1\right)$ and $C^{\prime }\left(-3,4\right)$ .