Answer:
The required algebraic rule of translation is [tex](x,y)\rightarrow (x-7,y+5)[/tex].
Step-by-step explanation:
The coordinates of a point are C(5, –4) and the coordinates of image are C’(–2, 1).
[tex]C(5,-4)\rightarrow C'(-2,1)[/tex] .... (1)
Let the algebraic rule of translation is
[tex](x,y)\rightarrow (x+a,y+b)[/tex] .... (2)
From (1) and (2) we get
[tex]x=5,y=-4[/tex]
[tex]x+a=-2[/tex]
[tex]5+a=-2[/tex]
[tex]a=-2-5[/tex]
[tex]a=-7[/tex]
The value of a is -7.
[tex]y+b=1[/tex]
[tex]-4+b=1[/tex]
[tex]b=1+4[/tex]
[tex]b=5[/tex]
The value of b is 5.
The algebraic rule of translation is
[tex](x,y)\rightarrow (x-7,y+5)[/tex]
Therefore the required algebraic rule of translation is [tex](x,y)\rightarrow (x-7,y+5)[/tex].
