From the info given we have the following coordinates for X, Y and Z
X=(7,11)
Y=(10,14)
Z=(8,7)
And we know that after a translation the coordinates of X' are:
X'=(5,11)
We need to find the function for the transformation so we can do this:
[tex]5=7+\Delta x[/tex][tex]\Delta x=5-7=-2[/tex][tex]11=11+\Delta y[/tex][tex]\Delta y=0[/tex]And then the transformation would be:
[tex]T\rightarrow(x-2,y)[/tex]With this transformation we can find the coordinates for Y' and Z' like this:
[tex]Y^{\prime}=(10-2,14)=(8,14)[/tex][tex]Z^{\prime}=(8-2,7)=(6,7)[/tex]So then the coordinates fo Z are (6,7)