Question

Using section formula, show that the points A(7, -5), B(9, -3) and C(13,1) are collinear.

Answer 1

Answer:

3 : 2

Step-by-step explanation:

Given Using section formula, show that the points A(7, -5), B(9, -3) and C(13,1) are collinear.

Let point C(13, 1) divide the other ratio k : 1. So we can take as m = k and n = 1

So x1 = 7, y1 = - 5, x2 = 9, y2 = - 3

We know that section formula is given by

(mx2 + nx1 /m + n , my2 + ny1 /m + n)

(13 , 1) = (9k + 7(1) / k +1 , -3k + (-5)1 / k + 1)

Equating the co ordinates to the respective numbers we get

9k + 7 / k + 1 = 13 ,  -3k - 5 / k + 1 = 1

 - 4k = 6                      -4k = 6

  k = - 3/2                   k = - 3/2

Since k is negative , it divides externally in the ratio 3 :2. Thus the points A,B and C are collinear.