Question

1. a figure was translated 2 units to the right and 3 units down. which rule represents this transformation?

options:
((x,y) \to (x - 3, y + 2))
((x,y) \to (2x, 3y))
((x,y) \to (3x, 2x))
((x,y) \to (x + 2, y - 3))
clear all

Explanation:

Step1: Recall translation rules

In coordinate geometry, translating a point \((x, y)\) \(h\) units right/left and \(k\) units up/down follows the rule \((x, y)\to(x + h, y + k)\), where \(h>0\) is right, \(h<0\) is left, \(k>0\) is up, \(k<0\) is down.

Step2: Apply given translation

Here, translation is 2 units right (\(h = 2\)) and 3 units down (\(k=- 3\)). So the rule is \((x,y)\to(x + 2,y-3)\).

Answer:

\((x,y)\to(x + 2,y - 3)\) (the last option among the given choices)