Given:
The composition of the translations is
[tex](T\langle-3,4\rangle \circ T\langle 8,-7\rangle )(x,y)[/tex]
To find:
The composition of the translations in one translations.
Solution:
We know that, [tex](T\langle-3,4\rangle \circ T\langle 8,-7\rangle)(x,y)[/tex] means [tex]T\langle 8,-7\rangle (x,y)[/tex] is followed by [tex]T\langle -3,4\rangle (x,y)[/tex].
In [tex]T\langle 8,-7\rangle (x,y)[/tex],
[tex](x,y)\to (x+8,y-7)[/tex]
So, [tex]P(x,y)\to P'(x+8,y-7)[/tex].
In [tex]T\langle -3,4\rangle (x,y)[/tex],
[tex](x,y)\to (x-3,y+4)[/tex]
[tex]P'(x+8,y-7)\to P''((x+8)-3,(y-7)+4)[/tex]
[tex]P'(x+8,y-7)\to P''(x+5,y-3)[/tex]
Now, after composition of the translations
[tex]P(x,y)\to P''(x+5,y-3)[/tex]
Here, rule of translation is
[tex](x,y)\to (x+5,y-3)[/tex]
Therefore, rule of translation is [tex]T\langle 5,-3\rangle (x,y)[/tex].
