Given:
The triangle A'B'C' is the image of triangle ABC after a translation as shown in the given graph.
To find:
The rule of translation in ARROW NOTATION.
Solution:
The general rule for translation is:
[tex](x,y)\to (x+a,y+b)[/tex] ...(i)
Where, a and b are constants.
From the given graph it is clear that the coordinate of point A are (2,3) and coordinates of point A' are (4,-2).
Using (i), the image of A(2,3) is
[tex]A(2,3)\to A'(2+a,3+b)[/tex]
We have, A'(4,-2).
[tex]A'(2+a,3+b)=A'(4,-2)[/tex]
On comparing both sides, we get
[tex]2+a=4[/tex]
[tex]a=4-2[/tex]
[tex]a=2[/tex]
And,
[tex]3+b=-2[/tex]
[tex]b=-2-3[/tex]
[tex]b=-5[/tex]
Putting [tex]a=2[/tex] and [tex]b=-5[/tex] in (i), we get
[tex](x,y)\to (x+2,y+(-5))[/tex]
[tex](x,y)\to (x+2,y-5)[/tex]
Therefore, the rule in ARROW NOTATION for the given translation is [tex](x,y)\to (x+2,y-5)[/tex].