Question

Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?
A) the terminal point of vector cu lies in quadrant II
B) the terminal point of vector cu lies in quadrant III
C) the terminal point of vector cu lies in quadrant I
D) the terminal point of vector cu lies in quadrant IV

Answer 1

The vector u is <9, 12> which means "start at any point, go to the right 9 units, and then up 12 units". If the starting point is point P = (0,0), then the terminal point is in quadrant I. For vector cu, the terminal point is now in quadrant III because we multiply the coordinates of (9,12) by some negative number c (eg: c = -1 so the terminal point is (-9,-12))

Answer: Choice B) terminal point of vector cu is in quadrant 3