The ratio in which the line 2x + y –4 = 0 divides the line segment joining the points A(2,–2) and B(3, 7) is .
A
2:9
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B
9:2
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C
2:7
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D
7:2
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Solution
The correct option is A 2:9 Let the line 2x+y-4 = 0 intersects the line segment AB at point C and C divides AB in the ratio k : 1. ∴ Coordinates of C will be (3k+2k+1,7k−2k+1) Also, point C lies on the line 2x+y-4 = 0, so it must satisfy its equation. ⇒2(3k+2k+1)+(7k−2k+1)=4⇒6k+4+7k−2k+1=4⇒13k+2=4k+4⇒9k=2⇒k=29