Question

1. a point p stays in the same location when it is reflected over line l. what can you conclude about point p?
2. determine a series of transformations that would map figure m onto figure n.

Explanation:

Step 1: Recall reflection property

A point that remains in the same location when reflected over a line lies on that line. So for point P reflected over line l, point P is on line l.

Step 2: Analyze transformation for figures M and N

1. First, note the orientation change. Figure M needs to be rotated 180° about the origin. The rule for a 180 - degree rotation about the origin is \((x,y)\to(-x,-y)\).
2. After rotation, we need to translate the figure. After rotating Figure M 180° about the origin, it needs to be translated 1 unit to the right and 1 unit down. The translation rule is \((x,y)\to(x + 1,y-1)\).

Answer:

1. Point P lies on line l.
2. Rotate Figure M 180° about the origin and then translate it 1 unit to the right and 1 unit down.