When transforming figures by translation, we use this formula of transformation:
[tex](x,y)\text{ }\rightarrow\text{ (x',y') = (x + A),(y + B)}[/tex]
Where,
A = is the translation of the x-coordinate either right or left.
(-) if going to the left
(+) if going to the right
B = is the translation of the y-coordinate either upward or downward.
(-) if going downward
(+) if going upward
The figure will be translated 10 to the right and 10 downward, thus, A = +10 and B = -10.
From the figure, the vertices are: A(-9,9), B(-3,9), C(-3,5), and D(-9,5).
Let's now identify the coordinates of the vertices of the translated figure:
At point A(-9,9):
[tex]\text{ }A\mleft(-9,9\mright)\text{ }\rightarrow\text{ A'(x',y') = }(x\text{+}A),(y+B)\text{ = (-9+10),(9-10) = (1,-1)}[/tex]
At point B(-3,9):
[tex]\text{ B}(-9,9)\text{ }\rightarrow\text{ B'(x',y') = }(x\text{+}A),(y+B)\text{ = (-3+10),(9-10) = (7,-1)}[/tex]
At point C(-3,5):
[tex]\text{ C}(-9,9)\text{ }\rightarrow\text{ C'(x',y') = }(x\text{+}A),(y+B)\text{ = (-3+10),(5-10) = (7,-5)}[/tex]
At point D(-9,5):
[tex]\text{ D}(-9,9)\text{ }\rightarrow\text{ D'(x',y') = }(x\text{+}A),(y+B)\text{ = (-9+10),(5-10) = (1,-5)}[/tex]
