Two lines in the xy-plane are drawn through the point (3,4) and the two trisection points of the line segment joining the points (-4,5) and (5,-1). Which of the following choices is the equation of one of these lines?
Solution
Between A & B, \triangle x = 9 and \triangle y = 6. Consult the figure below.
So, T1 = ( 4 + 3, 5 – 2) = (-1,3), and
T2 = (-4 + 6, 5 – 4) = (2, 1)
We find the slopes of T1P and T2P and see if they match the given equations’ slopes.
Slope T1P:
m = (4 – 3)/(3 – ( 1)) = 1/4 (e?)
Slope T2P:
m = (4 – 1)/(3 – 2) = 3/1 = 3 (nope)
So it seems to be (e).
Check: e): x – 4y + 13 = 0 Does it contain T1? -1 – 4(3) + 13 = 0 OK.
Does it have P? 3 – 4(4) + 13 OK.
It is, in fact, e).