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Question

Question 1
Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

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Solution

Let us assume that the line 2x + y – 4 = 0 divides the line segment AB in the ratio k : 1.
Coordinates of the point of division can be given as follows using section formula:
x=2+3kk+1
y=2+7kk+1
Substituting the values of x and y in following equation:
2x+y4=0
2(2+3kk+1)+(2+7kk+1)4=0
4+6kk+1+(2+7kk+1)4=0
4+6k2+7k4(k+1)=0
4+6k2+7k4k4=0
2+9k=0
9k=2
k=29


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