If (k,1) , (0,d) , (1,1) are collinear then find 1/k + 1/d =---

Answer 1

if collinear, then their slopes must be equal

(d-1)/-k = (1-1)/(1-k) = (1-d)/(1)

(1-d)/k = 0/(1-k) = (1-d)/1

from the middle ratio we know that the slope = 0
and thus all numerators are 0
so 1 - d = 0
d = 1

similarly if the first and the last are equal,
(1-d)/k = (1-d)/1 , then k = 1

so the three points are (1,1) (0,1) and (1,1)
which are collinear, so
1/k + 1/d = 2