The image of the triangle and the rule for the transformation of the segments are;
13. The coordinates of the vertices of the image of the triangle are; (-3, 1), (2, 4), and (-6, 5)
Please find attached the diagram of the image of the triangle, following a transformation (x, y) → (x + 3, y + 2) created with MS Excel
16. The translation rule if the red line is the image is; T(1, -3)
The steps to obtain the image and the translation rule are as follows;
13. The coordinate points of the vertices of the triangle are;
(-6, -1), (-1, 2), and (-9, 3)
The coordinates of the image of the triangle following the translation (x, y) → (x + 3, y + 2)
Therefore, the coordinates of the vertices of the image are;
(-6, -1) → (x + 3, y + 2) → (-3, 1)
(-1, 2) → (x + 3, y + 2) → (2, 4)
(-9, 3) → (x + 3, y + 2) → (-6, 5)
The above coordinate points can be used to plot the image of the triangle
16. The coordinate of the vertices of the red segments are; (0, 0), (5, -1)
The coordinate of the vertices of the image are; (-1, 3), (4, 2)
The rule for the translation rule if the red line is the image is therefore;
T(0 - (-1), 0 - 3) = T(1, -3)