Suppose point D has coordinates $(x,y)$. After a translation by $(3,-2)$, what is the new y-coordinate of point D?

• A. $y+3$
• B. $y-3$
• C. $y+2$
• D. $y-2$

Answer: (D)

Verified step by step guidance

1. Recall that a translation moves every point of a figure or a space by the same distance in a given direction. The translation vector here is (3, -2), meaning we move 3 units in the x-direction and -2 units in the y-direction.
2. The original coordinates of point D are given as (x, y). After translation, the new coordinates (x', y') are found by adding the translation vector components to the original coordinates.
3. Calculate the new x-coordinate by adding 3 to the original x: \(x' = x + 3\).
4. Calculate the new y-coordinate by adding -2 to the original y: \(y' = y + (-2)\), which simplifies to \(y' = y - 2\).
5. Therefore, the new y-coordinate of point D after the translation is expressed as \(y - 2\).