Question

if  (-8,4),(2,4)and(5,a)   collinear    point then   find  the  value  of  a

Answer 1

a= 4

three points are said to be collinear, if they all lie in straight line..
also, the slope should be same..

slope = (y2-y1) / (x2-x1)

so, for eg., say if a= (-8,4) , b= (2,4) and c=(5,a)

ab = (4-4)/(2-4) = 0/-2 = 0

bc = (a-4/5-2) = (a-4)/3 = 0 (since slope is "0" for ab)
       (a-4) = 0
         a = 4

ac = (a-4)/(5+8) = 0 (since slope is "0" for ab)
     a-4/13 = 0
       a-4 = 0
       a = 4

      

Answer 2

Three points are said to be collinear, if they all lie in straight line..
slope of the line passing through the points is given by

slope = (y2-y1) / (x2-x1)

let us take the points  a= (-8,4) , b= (2,4) and c=(5,a)
first finding the slope of the line passing through a and b

ab = (4-4)/(2-4)
= 0/-2
= 0
next finding the slope of the line passing through the points b and c

bc = (a-4/5-2) =
 (a-4)/3
= 0 (since slope is "0" for ab)
so we have
       (a-4) = 0
         a = 4        (Adding 4 on both sides)
slope of the line passing through the points a and c is

ac = (a-4)/(5+8) = 0 (since slope is "0" for ab)
     a-4/13 = 0
       a-4 = 0
       a = 4