To find the new coordinates of \( E' \) after translating \( E \) right by 44 units and up by 32 units, you can add the respective values to the x and y coordinates of the original point \( E \).
Given:
- Original point \( E = (3, -2) \)
- Translation right (x-axis) = +44
- Translation up (y-axis) = +32
You perform the calculations as follows:
-
For the x-coordinate: \[ 3 + 44 = 47 \]
-
For the y-coordinate: \[ -2 + 32 = 30 \]
Putting it together, the coordinates of \( E' \) are: \[ E' = (47, 30) \]
Thus, \( E' = (47, 30) \).