In each of the following, find the value of a for which the given points are collinear. 

(ii) (a-3-2a), (-a+1,2a) and (-4-a,6-2a)

Asked by dvijaybs45 | 7th Sep, 2020, 08:57: PM

Expert Answer:

Question: (a, 2 - 2a), (-a+1,2a) and (-4-a,6-2a)

Solution:
 
begin mathsize 16px style Since space the space points space are space collinear.
rightwards double arrow Area space of space straight a space Triangle space equals space 0
rightwards double arrow 1 half open square brackets straight x subscript 1 open parentheses straight y subscript 2 minus space straight y subscript 3 close parentheses plus space straight x subscript 2 open parentheses straight y subscript 3 minus space straight y subscript 1 close parentheses space plus space straight x subscript 3 open parentheses straight y subscript 1 minus space straight y subscript 2 close parentheses close square brackets equals space 0
rightwards double arrow straight a open parentheses 2 straight a minus space 6 space plus space 2 straight a close parentheses plus space open parentheses negative straight a plus 1 close parentheses open parentheses 6 minus 2 straight a minus 2 plus 2 straight a close parentheses space plus space open parentheses negative 4 minus straight a close parentheses open parentheses 2 minus 2 straight a space minus space 2 straight a close parentheses space equals space 0
rightwards double arrow 8 straight a squared plus space 4 straight a space minus space 4 space equals space 0
rightwards double arrow 2 straight a squared plus space straight a space minus space 1 space equals space 0
rightwards double arrow left parenthesis 2 straight a space minus space 1 right parenthesis left parenthesis straight a space plus space 1 right parenthesis space equals space 0
rightwards double arrow left parenthesis 2 straight a space minus space 1 right parenthesis space equals space 0 space or space space left parenthesis straight a space plus space 1 right parenthesis space equals space 0 space rightwards double arrow straight a space equals space 1 half space or space straight a equals space minus 1
end style

Answered by Yasmeen Khan | 9th Sep, 2020, 11:08: AM