Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7) - Mathematics

Sum

Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)

Solution

Suppose the line 3x + y – 9 = 0 divides the line segment joining A (1, 3) and B(2, 7) in the ratio k : 1 at point C. Then, the coordinates of C are

( \frac{2k+1}{k+1},\ \frac{7k+3}{k+1})

But, C lies on 3x + y – 9 = 0. Therefore,

3( \frac{2k+1}{k+1})+\frac{7k+3}{k+1}-9=0

⇒ 6k + 3 + 7k + 3 – 9k – 9 = 0

⇒ k = \frac { 3 }{ 4 }

So, the required ratio is 3 : 4 internally

Type III : On determination of the type of a given quadrilateral

Concept: Section Formula
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