Answer:
Triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'. The rule of translation is
[tex](x,y)\rightarrow (x-1,y-1)[/tex]
Step-by-step explanation:
Given information: In triangle ABC, A(-5,1), B(-2,7), C(0,1). In triangle A'B'C', A'(-6,0), B'(-3,6), C'(-1,0).
Let the rule of translation be
[tex](x,y)\rightarrow (x-a,y-b)[/tex]
where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b<0, then the graph shifts b units up and if b>0, then the graph shifts b units down.
It is given that A(-5,1) and A'(-6,0).
[tex]A(-5,1)\rightarrow A'(-5-a,1-b)[/tex]
[tex]A'(-6,0)=A'(-5-a,1-b)[/tex]
On comparing both sides, we get
[tex]-6=-5-a\Rightarrow a=1[/tex]
[tex]0=1-b\Rightarrow b=1[/tex]
The value of a is 1 and value of b is 1. So, the rule of translation is
[tex](x,y)\rightarrow (x-1,y-1)[/tex]
Therefore the triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'.
