Question

a person facing east walks east 20 paces, turns, walks north 10 paces, turns, walks west 25 paces, turns, walks south 10 paces, turns, walks east 15 paces, and then stops. what one transformation could have produced the same final result in terms of the position of the person and the direction the person faces?
translation (x, y)→(x + 10, y + 5)
translation (x, y)→(x + 10, y)
rotation (x, y)→(-y, x)
reflection (x, y)→(x, y)

Explanation:

Step1: Analyze east - west movement

The person walks east 20 paces, then west 25 paces, and then east 15 paces. The net east - west displacement is \(20 - 25+15=10\) paces east.

Step2: Analyze north - south movement

The person walks north 10 paces and then south 10 paces. The net north - south displacement is \(10 - 10 = 0\) paces.

Step3: Determine the transformation

Since the net displacement in the x - direction (east - west) is 10 paces east and in the y - direction (north - south) is 0 paces, the transformation is \((x,y)\to(x + 10,y)\).

Answer:

Translation \((x,y)\to(x + 10,y)\)