Question

rectangle abcd has vertices a(-6, -2), b(-3, -2), c(-3, -6), and d(-6, -6). the rectangle is translated so that the coordinates of the image are a(-10, 1), b(-7, 1), c(-7, -3), and d(-10, -3).

which rule was used to translate the image?

\\(t_{-4, 3}(x, y)\\)
\\(t_{-4, 1}(x, y)\\)
\\(t_{4, -1}(x, y)\\)
\\(t_{4, -3}(x, y)\\)

Explanation:

Calculate coordinate shifts

$$
LATEXBLOCK0
$$

Verify shifts with another vertex

$$
LATEXBLOCK1
$$

Match with translation notation

$$ T_{a, b}(x, y) = (x + a, y + b) \implies T_{-4, 3}(x, y) $$

Answer:

• (A) \(T_{-4, 3}(x, y)\) (Correct answer)
• (B) \(T_{-4, 1}(x, y)\)
• (C) \(T_{4, -1}(x, y)\)
• (D) \(T_{4, -3}(x, y)\)