Question

find the value of m if the point m if the points (5,1) (2,3) and (8,2m) are collinear​

Answer 1

Answer:

19/14

Step-by-step explanation:

Let A≡(x1,y1)≡(5,1),B≡(x2,y2)≡(−2,−3),C≡(x3,y3)≡(8,2m)

Since , the points A ≡(5,1),B≡(−2,−3)andC≡(8,2m) are collinear.

∴ Area of △ABC=0

⇒12[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]=0

⇒12[5(−3−2m)+(−2)(2m−1)+8{1−(−3)}]=0

⇒12(−15−10m−4m+2+32)=0

⇒12(−14m+19)=0⇒m=19/14

Hence , the required value of m is 19/14.