Answer:
The image of [tex](7,2)[/tex] is [tex](2,12)[/tex]
Step-by-step explanation:
First you need to find the translation vector.
Let the translation vector be [tex]u=(a,b)[/tex]. Then the translation rule is
[tex](x,y)\to (x+a,y+b)[/tex].
From the equation, the image of [tex]P(2,-4)[/tex] is [tex]P'(-3,6)[/tex].When we apply this rule using the translation vector, we get
[tex]P(2,-4)\to P'(2+a,-4+b)[/tex]
Now we have
[tex]P'(2+a,-4+b)=P'(-3,6)[/tex]
We can therefore equate corresponding coordinates
[tex]2+a=-3[/tex] and [tex]-4+b=6[/tex]
This implies that:
[tex]a=-3-2[/tex] and [tex]b=6+4[/tex]
[tex]a=-5[/tex] and [tex]b=10[/tex]
Hence our translation vector is [tex]u=(-5,10)[/tex]
The translation rule now becomes:
[tex](x,y)\to (x-5,y+10)[/tex].
To find the image of (7,2), we plug it into the translation rule.
[tex](7,2)\to (7-5,2+10)[/tex].
[tex](7,2)\to (2,12)[/tex].
