Question

transformations test (topic 4)
the rule ( t_{(3, 2)} ) is used for point ( (5, -1) ). where is the translated point in the coordinate system?
☐ quadrant i
☐ quadrant ii
☐ quadrant iii
☐ quadrant iv

Explanation:

Step1: Understand translation rule

The translation rule \( T_{(a,b)} \) means we add \( a \) to the \( x \)-coordinate and \( b \) to the \( y \)-coordinate of the point. But wait, maybe there's a typo, and the rule is \( T_{(-3, 2)} \) (assuming common translation notation). Let's assume the translation is \( T_{-3,2} \) (shifting \( x \) by -3, \( y \) by +2). The original point is \( (5, -1) \).

Step2: Apply translation

For the \( x \)-coordinate: \( 5 + (-3) = 2 \)
For the \( y \)-coordinate: \( -1 + 2 = 1 \)
So the translated point is \( (2, 1) \).

Step3: Determine quadrant

In the coordinate system, Quadrant I has \( x>0 \) and \( y>0 \). Since \( 2>0 \) and \( 1>0 \), the point \( (2,1) \) is in Quadrant I.

Answer:

Quadrant I