A translation is a rigid transformation, therefore, the distances between every pair of points in the preimage and the distances between the corresponding points in the image are congruent
The completed table is presented as follows;
[tex]\begin{array}{|c|c|c|c|}\underline{\mathbf{x}}&\underline{\mathbf{y}}&\underline{\mathbf{new \ x}}&\underline{ \mathbf{new \ y}}\\1&1&6&4\\3&1&8&4\\3&2&8&5\\2&2&7&5\\2&4&7&7\\1&4&6&7 \end{array}\right][/tex]
Required: To enter the coordinates in the given table that translates the original shape 5 units to the right and 3 units up
Solution:
The coordinates of the image, following the translation of the preimage in the x, y plane a given number of units in the x, and y direction, involves adding those units to the coordinates of the preimage, so the two images remain similar as follows;
[tex]\begin{array}{|c|c|c|c|}\underline{\mathbf{x}}&\underline{\mathbf{y}}&\underline{\mathbf{new \ x}}& \underline{\mathbf{new \ y}}\\1&1&1 + 5 = 6&1 + 3 = 4\\3&1&3 + 5 = 8&1 + 3 = 4\\3&2&3 + 5 = 8&2 + 3 = 5\\2&2&2 + 5 = 7&2 + 3 = 5\\2&4&2 + 5 = 7&4 + 3 = 7\\1&4&1 + 5 = 6&4 + 3 = 7 \end{array}\right][/tex]
Therefore, the coordinates of the vertices of the image are;
(6, 4), (8, 4), (8, 5), (7, 5), (7, 5), (7, 7), and (6, 7)
Learn more about translation transformation here:
https://brainly.com/question/18758717
