Using section formula show that the points are collinear
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Using section formula, show that the points A(7, -5), B(9, -3) and C(13,1) are collinear.
Asked by admin @ in Math viewed by 362 People
Using section formula, show that the points A(7, -5), B(9, -3) and C(13,1) are collinear.
Answered by admin @
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.
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