Given the vertices of RST where R (3, 2), S (-1, 1) and T (0, 4), explain how you would solve for R’S’T’ after the translation
(x, y) (x +3, y – 1).
To find the coordinates of R'S'T' after the translation (x, y) → (x + 3, y - 1), you can apply the translation vector (3, -1) to each of the original coordinates (R, S, T).
Step 1: Apply the translation vector to the x-coordinate of each point.
- For vertex R (3, 2), add 3 to the x-coordinate: 3 + 3 = 6.
- For vertex S (-1, 1), add 3 to the x-coordinate: -1 + 3 = 2.
- For vertex T (0, 4), add 3 to the x-coordinate: 0 + 3 = 3.
Step 2: Apply the translation vector to the y-coordinate of each point.
- For vertex R (3, 2), subtract 1 from the y-coordinate: 2 - 1 = 1.
- For vertex S (-1, 1), subtract 1 from the y-coordinate: 1 - 1 = 0.
- For vertex T (0, 4), subtract 1 from the y-coordinate: 4 - 1 = 3.
Step 3: Write down the new coordinates for R', S', T':
- R' has coordinates (6, 1).
- S' has coordinates (2, 0).
- T' has coordinates (3, 3).
Therefore, the new coordinates after the translation are R'(6, 1), S'(2, 0), and T'(3, 3).
To solve for R’S’T’ after the given translation (x, y) → (x + 3, y – 1), we will apply the same translation to the coordinates of the original vertices R, S, and T.
Let's start with the original vertices:
R(3, 2), S(-1, 1), T(0, 4)
To find the coordinates of the translated vertices R'S'T', we will apply the translation (x, y) → (x + 3, y – 1) to each vertex.
For R:
x-coordinate of R' = x-coordinate of R + 3
y-coordinate of R' = y-coordinate of R - 1
x-coordinate of R' = 3 + 3 = 6
y-coordinate of R' = 2 - 1 = 1
So the coordinates of R’ are (6, 1).
For S:
x-coordinate of S' = x-coordinate of S + 3
y-coordinate of S' = y-coordinate of S - 1
x-coordinate of S' = -1 + 3 = 2
y-coordinate of S' = 1 - 1 = 0
So the coordinates of S’ are (2, 0).
For T:
x-coordinate of T' = x-coordinate of T + 3
y-coordinate of T' = y-coordinate of T - 1
x-coordinate of T' = 0 + 3 = 3
y-coordinate of T' = 4 - 1 = 3
So the coordinates of T’ are (3, 3).
Therefore, the vertices of R’S’T’ after the translation are R’(6, 1), S’(2, 0), and T’(3, 3).