Given:
The graph of a translation. X'Y' is a translation of XY.
To find:
The rule of the translation.
Solution:
Let the rule of the translation be
[tex](x,y)\to (x+a,y+b)[/tex] ...(i)
So, we need to find the value of a and b.
From the given graph, it is clear that X(-4,-9) and X'(-1,0).
Using (i), the image of X(-4,-9) is
[tex]X(-4,-9)\to X'(-4+a,-9+b)[/tex]
We have, X'(-1,0). So,
[tex]X'(-4+a,-9+b)=X'(-1,0)[/tex]
On comparing both sides, we get
[tex]-4+a=-1[/tex]
[tex]a=-1+4[/tex]
[tex]a=3[/tex]
And,
[tex]-9+b=0[/tex]
[tex]b=9[/tex]
So, the missing values in the rule of the translation are 3 and 9 respectively.
Therefore, the rule of translation is [tex](x,y)\to (x+3,y+9)[/tex].
