Question

the rule ( t_{<-6,4>} ) is used for point ( (2,-7) ). where is the translated point in the coordinate system?
( \bigcirc ) quadrant iii
( \bigcirc ) quadrant i
( \bigcirc ) quadrant ii
( \bigcirc ) quadrant iv

Explanation:

Step1: Understand the translation rule

The translation rule \( T_{\langle -6, 4
angle} \) means we subtract 6 from the x - coordinate and add 4 to the y - coordinate of the point.
For the point \((x,y)=(2,-7)\), the new x - coordinate \( x'=x - 6=2-6=- 4\) and the new y - coordinate \( y'=y + 4=-7 + 4=-3\).

Step2: Determine the quadrant

In the coordinate system, Quadrant III is where both the x - coordinate and y - coordinate are negative. Since the translated point is \((-4,-3)\) with \(x'=-4<0\) and \(y'=-3<0\), it lies in Quadrant III.

Answer:

Quadrant III