in each of the following find the value of k for which the points are collinear . 1) (7,-2), (5,1) ,(3,k)

Asked by jaiharekrushna75 | 11th Sep, 2020, 11:56: AM

Expert Answer:

Let A(7,-2), B(5,1) and C(3,k) be three collinear points.
 
Area of a ΔABC =0
 begin mathsize 16px style 1 half open square brackets straight x subscript 1 open parentheses straight y subscript 2 minus straight y subscript 3 close parentheses plus straight x subscript 2 open parentheses straight y subscript 3 minus straight y subscript 2 close parentheses plus space straight x subscript 3 open parentheses straight y subscript 1 minus straight y subscript 2 close parentheses space close square brackets space equals space 0
rightwards double arrow 7 left parenthesis 1 minus straight k right parenthesis space plus space 5 open parentheses straight k space plus space 2 close parentheses plus space 3 left parenthesis negative 2 minus 1 right parenthesis space equals space 0
rightwards double arrow 7 space minus space 7 straight k space plus space 5 straight k space plus space 10 space minus 9 space equals space 0
rightwards double arrow negative 2 straight k plus 8 space equals space 0
rightwards double arrow space straight k space equals space 4 end style

Answered by Yasmeen Khan | 11th Sep, 2020, 01:10: PM