find the ratio in which the line 3x+y_9= 0 divides the line segment joining the points A (1,3)&(2,7)
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Let the line 3x+y-9=0 divides the line segment joining the points (1,3) and (2,7) at a point X in the ratio k:1
BY section formula, the coordinates of X are
X(2k+1/k+1,7k+3/k+1) and this point lies on the line 3x +y-9
∴3(2k+1/k+1)+(7k+3/k+1)-9=0
6k+3+7k+3-9k-9=0
4k-3=0
k=3/4
Ans therefore the line segment is givided inj the ratio 3:4
BY section formula, the coordinates of X are
X(2k+1/k+1,7k+3/k+1) and this point lies on the line 3x +y-9
∴3(2k+1/k+1)+(7k+3/k+1)-9=0
6k+3+7k+3-9k-9=0
4k-3=0
k=3/4
Ans therefore the line segment is givided inj the ratio 3:4
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