Answer:
C. (x, y) → (x + 1, y - 7)
Step-by-step explanation:
To find the algebraic rule describing the translation from triangle STU to triangle S'T'U', we can select a vertex from ΔSTU and its corresponding vertex in ΔS'T'U', and then observe the horizontal and vertical displacement in units.
Let's choose points S and S'. The coordinates of point S are (3, 7) and the coordinates of point S' are (4, 0).
The horizontal translation is the difference between the x-coordinates of the translated point and the original point. In this case, the x-coordinate of point S' is 4 and the x-coordinate of point S is 3. So, the horizontal translation is:
[tex]\textsf{Horizontal translation} = x_{S'} - x_S = 4 - 3 = 1[/tex]
The vertical translation is the difference between the y-coordinates of the translated point and the original point. In this case, the y-coordinate of point S' is 0 and the y-coordinate of point S is 7. So, the vertical translation is:
[tex]\textsf{Vertical translation} = y_{S'} - y_S = 0 - 7 = -7[/tex]
If we have a point with coordinates (x, y) and we want to translate it horizontally by a units and vertically by b units, the new coordinates will be (x + a, y + b).
So, in this case:
- Horizontal translation: Add 1 to the x-coordinate.
- Vertical translation: Subtract 7 from the y-coordinate.
Therefore, the algebraic rule that describes the translation of ΔSTU to ΔS'T'U' is:
[tex]\Large\boxed{\boxed{(x, y)\longrightarrow (x+1,y-7)}}[/tex]
