Coordinate Geometry
RD Sharma
CBSE
Grade 10
Question:
The line $2x + y - 4 = 0$ divides the line segment joining $A(2, -2)$ and $B(3, 7)$ in the ratio:
(a) $2 : 9$
(b) $9 : 2$
(c) $2 : 3$
(d) $3 : 2$
Step-by-Step Solution
Key Concept: Ratio $= -\dfrac{2(2) + (-2) - 4}{2(3) + 7 - 4} = -\dfrac{4 - 6}{6 + 7 - 4} = -\dfrac{-2}{9} = \dfrac{2}{9} \Rightarrow 2 : 9$.
Let ratio be $k : 1$. $x = \dfrac{3k+2}{k+1}, y = \dfrac{7k-2}{k+1}$. Substitute: $2(3k+2) + (7k-2) - 4(k+1) = 0 \Rightarrow 6k+4+7k-2-4k-4 = 0 \Rightarrow 9k - 2 = 0 \Rightarrow k = 2/9$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $k = 2/9 \Rightarrow 2 : 9$: 1.0 Mark
Correct Answer: $2 : 9$
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