The coordinates of the point are (-1, -6).
Step-by-step explanation:
Step 1:
We need to plot the points for both triangles PQR and [tex]P^{1} Q^{1} R^{1}[/tex].
The points of the triangle PQR are P (1, 6), Q (3, 2), and R (1, 2).
The points of the triangle [tex]P^{1} Q^{1} R^{1}[/tex] are [tex]P^{1}[/tex] (-6, 7), [tex]Q^{1}[/tex](-4, 3), and [tex]R^{1}[/tex](-6, 3).
Step 2:
Now we determine translation of the coordinates.
P (1, 6) becomes [tex]P^{1}[/tex] (-6, 7).
Q (3, 2) becomes [tex]Q^{1}[/tex](-4, 3).
R (1, 2) becomes [tex]R^{1}[/tex](-6, 3).
So the translation is (x, y) becomes (x - 7, y + 1).
Step 3:
Now we determine the coordinates of square STUV.
The points of the square STUV are S (6, -3), T (6, -7), U (2, -3), and V (2, -7).
The translation is (x, y) becomes (x - 7, y + 1).
For S (6, -3). x = 6 - 7 = -1, y = -3 + 1 = -2, So [tex]S^{1}[/tex] becomes (-1, -2).
For T (6, -7). x = 6 - 7 = -1, y = -7 + 1 = -6, So [tex]T^{1}[/tex] becomes (-1, -6).
For U (2, -7). x = 2 - 7 = -5, y = -7 + 1 = -6, So [tex]U^{1}[/tex] becomes (-5, -6).
For V (2, -3). x = 2 - 7 = -5, y = -3 + 1 = -2, So [tex]V^{1}[/tex] becomes (-5, -2).
So coordinates of the point [tex]T^{1}[/tex] are (-1, -6).
