Question

Using Section formula prove that (2,5) , (4,6) and (8,8) are collinear.

Answer 1

Given: Points =  (2,5) , (4,6) and (8,8)

To find: Using Section formula prove that (2,5) , (4,6) and (8,8) are collinear.

Solution:

• Let the points be: A(2,5) , B(4,6) and C(8,8)

• Point A, B, C are collinear if C divides AB in some ratio, so let the ratio be k:1.

• So we know the ratio that (mx2+n1)/m+n, (my2+ny1)/m+n.

• Putting the values in the formula we get:

         k(4) + 1(2)/ k+1, k(6) + 1(5)/ k+1

         equating this with the point C, we get:

         4k + 2/ k+1 = 8,  6k+5/k+1 = 8

         4k + 2= 8k+8,  6k+5=8k+8

         -6 = 4k, -3 = 2k

         k = -3/2

Answer:

              So the value of k is same from both the terms, so the points are collinear.