Question

which image is a reflection of the polygon in quadrant i?

Explanation:

Step1: Recall reflection property

Reflection over the \(x -\)axis changes the \(y -\)coordinate sign (\((x,y)\to(x, - y)\)), over the \(y -\)axis changes the \(x -\)coordinate sign (\((x,y)\to(-x,y)\)).

Step2: Analyze quadrants

Quadrant I: \(x>0,y > 0\); Quadrant II: \(x<0,y>0\); Quadrant III: \(x < 0,y<0\); Quadrant IV: \(x>0,y<0\).
The polygon in Quadrant I has \(x>0,y>0\). A reflection over the \(y -\)axis gives \(x<0,y>0\) (Quadrant II), over the \(x -\)axis gives \(x>0,y<0\) (Quadrant IV).
But for a reflection (assuming reflection over \(y -\)axis as per visual symmetry - same \(y -\) values, opposite \(x -\) values in terms of sign).

Answer:

the polygon in Quadrant II