Question

geometry topics 1-6 benchmark assessment
the rule t is applied to point (2, -2). in which part of the coordinate system is the translated point located?
show your work here
○ quadrant i ○ quadrant ii
○ quadrant iii ○ quadrant iv

which triangle is congruent to △pqr?
image of two triangles on a grid

Explanation:

Step1: Understand Translation Rule

The translation rule \( T_{-3, -5} \) means we subtract 3 from the x - coordinate and 5 from the y - coordinate of the original point. The original point is \( (2, - 2) \).

Step2: Apply Translation to x - coordinate

For the x - coordinate: \( 2-3=-1 \)

Step3: Apply Translation to y - coordinate

For the y - coordinate: \( - 2-5=-7 \)

Step4: Determine Quadrant of Translated Point

The translated point is \( (-1, - 7) \). In the coordinate system, Quadrant III has both x and y coordinates negative. So the translated point is in Quadrant III.

Answer:

quadrant III