Answer:
Part) A. Part B and Part C see the explanation
Explanation:
Part A) Translate Triangle ABC 6 units horizontally How are the values in the ordered pairs affected by the translation?
If the translation is 6 units horizontally, that means that each vertex of the ABC pre-image is going to move 6 units to the right, i.e. each x-coordinate of the ABC pre-image is going to increase by 6 units and each y-coordinate of the ABC pre-image is going to remain the same.
Part B) Translate Triangle ABC -3 units vertically How are the values in the ordered pairs affected by the translation?
If the translation is -3 units vertically, that means that each vertex of the ABC pre-image is going to move 3 units down, i.e. each x-coordinate of the ABC pre-image is going to remain the same and each y-coordinate of the ABC pre-image is going to decrease by 6 units.
Part C) How could you determine the coordinates of the vertices of a translated image without using a graph?
we know that
The coordinates of the image vertices can be determined through the rule of the translation
so
In the part A) the translation is +6 units horizontally (6 units at right)
therefore
The rule of the translation of the pre-image to the image is equal to
(x,y) ------> (x+6,y)
Example
The coordinates of the pre-image A(-4,1)
To obtain the coordinates of the image A' apply the rule of the translation
A(-4,1)--------> A'(-4+6,1)
A(-4,1)--------> A'(2,1)
In the part B) the translation is -3 units vertically (3 units down)
therefore
The rule of the translation of the pre-image to the image is equal to
(x,y) ------> (x,y-3)
Example
The coordinates of the pre-image A(-4,1)
To obtain the coordinates of the image A' apply the rule of the translation
A(-4,1)--------> A'(-4,1-3)
A(-4,1)--------> A'(-4,-2)