Answer:
a) The vertices of the triangle G'H'I' are , and , respectively.
b) The triangle G''H''I'' have vertices at , and .
Step-by-step explanation:
a) From Linear Algebra, we define the translation by the following vector:
(1)
Where:
- Original point, dimensionless.
- Translated point, dimensionless.
- Translation vector, dimensionless.
If we know that , , and , then the vertices of the triangle G'H'I' are, respectively:
(2)
(3)
(4)
The vertices of the triangle G'H'I' are , and , respectively.
b) From Linear Algebra, we define the reflection with respect to a horizontal line as follows:
(5)
Where:
- Original point, dimensionless.
- Reflection point, dimensionless.
If we know that and , then the location of point G'' is:
(6)
If we know that and , then the location of the point H'' is:
(7)
If we know that and , then the location of the point I'' is:
(8)
The triangle G''H''I'' have vertices at , and .