Question

Suppose the point x,y is translated vertically d units. Write the coordinates of the image of the point.

a) (x,y+d)
b) (x−d,y)
c) (x,y−d)
d) (x+d,y)

Answer 1

The coordinates of a point (x,y) translated vertically d units upward would be (x, y+d), and if it's translated downward, the coordinates would be (x, y-d).

Step-by-step explanation:

If the point (x,y) is translated vertically d units, the coordinates of the image of the point depend on the direction of the translation. Vertical translation means moving the point up or down along the y-axis without changing its x-coordinate. Therefore, if the translation is upward by d units, the new y-coordinate will be y+d. If it is downward, the y-coordinate will be y-d. The x-coordinate remains unchanged in a vertical translation.

Accordingly, the correct answer is:

• (a) (x, y+d) for vertically upward translation in the coordinate system.
• (c) (x, y-d) for vertically downward translation in the coordinate system.

Options (b) and (d) would represent horizontal translations, which are not the case here.