Question

Use the motion rule (x, y) + (x - 2, y + 2), which means translate the line segment 2 units to the right and 2 units up. What will be the new coordinates of the point (4, 3) after applying this rule?

a) (2, 1)
b) (6, 5)
c) (6, 1)
d) (2, 5)

Answer 1

The new coordinates of the point (4, 3) after applying the translation (x - 2, y + 2) are (2, 5), which is option d).

Step-by-step explanation:

The student is asking how to apply a translation to a point on a coordinate plane according to the given motion rule: (x, y) + (x - 2, y + 2). This rule indicates that to get the new coordinates, we add -2 to the x-coordinate and +2 to the y-coordinate of the original point.

To apply this to the point (4, 3), we subtract 2 from the x-coordinate (which is 4) and add 2 to the y-coordinate (which is 3):

• New x-coordinate: 4 - 2 = 2
• New y-coordinate: 3 + 2 = 5

Therefore, the new coordinates after applying the motion rule are (2, 5), which corresponds to option d).