Point A is the terminal point of angle phi and point B is the terminal point of angle theta. Point A is in the first quadrant and point B is in the second quadrant, while tan phi = 1 and tan theta = -7. Find the slope of AB.

Question

Ok so since A is in the first quadrant and tan phi = 1, thus A must be point (sqrt2 / 2, sqrt2 / 2).
B is in the second quadrant but where?

Thanks

Answer 1

for A, tan phi = 1 = 1/2
so point A is (1,1)

since tanØ = -7 = -7/1 and Ø is in II
then point B is (-7,1)

so slope of AB = (1-1)/(-7-1) = 0

BUT, this is a poorly worded question
What if point A is (5,5)
notice that tan phi = 5/5 = 1
You were also correct in saying A is (√2/2, √2/2)
as a matter of fact , A could be any point on the line
y = x

Same thing is true for B,
B could also be (-14,2) , etc

Really silly question, slope AB could be anything