Xavier starts 5 feet away from a motion detector. He then walks away from the detector at a rate of 0.5 ft/sec for 4 seconds. He remains still for 2 seconds, and then walks toward the detector at a rate of −2 ft/sec for 3 seconds. How far in feet is Xavier from the motion detector when he finishes his walk?

1 foot away from motion detector

Step-by-step explanation:

Given that:

Initial Position = 5 feets away from detector

Distance moved away = 0.5ft/sec for 4 seconds ; distance moved away = 0.5 * 4 = 2 feets

Total distance away = 5 feets + 2 feets = 7 feets

Distance moved towards motion detector :

-2 ft/sec for 3 seconds ;

Distance = speed * time

Distance moved = (-2ft/sec * 3) = - 6 feets

Hence, distance in feets from motion detector :

7 feets - 6feets = 1 feet away from motion detector

(A)

Step-by-step explanation:

Point A is at (-2,4)

Rule of a 180° rotation about the origin: (x,y) --> (-x,-y)

Using the rule, (-2,4) will become (2,-4).

A' should be (2,-4) or Option A.