The ΔABC has the following coordinates:
[tex]\begin{gathered} A=(-4,5) \\ B=(1,4) \\ C=(0,-3) \end{gathered}[/tex]
The triangle undergoes a translation to the right and down.
If a point is shifted "a" units to the right, the transformation rule is given to be:
[tex](x,y)\to(x+a,y)[/tex]
If a point is shifted "b" units down, the transformation rule is given to be:
[tex](x,y)\to(x,y-b)[/tex]
Combining both rules, we have:
[tex](x,y)\to(x+a,y-b)[/tex]
If the original points are translated 3 units to the right and 7 units down, we will have:
[tex]\begin{gathered} a=3 \\ b=7 \end{gathered}[/tex]
Hence, the rule becomes:
[tex](x,y)\to(x+3,y-7)[/tex]
Therefore, the new coordinates are:
[tex]\begin{gathered} A^{\prime}\to(-4+3,5-7)=(-1,-2) \\ B^{\prime}\to(1+3,4-7)=(4,-3) \\ C^{\prime}\to(0+3,-3-7)=(3,-10) \end{gathered}[/tex]
