Coordinate Geometry
RD Sharma
CBSE
Grade 10
Question:
If the point $C(-1, 2)$ divides internally the line segment joining $A(2, 5)$ and $B(x, y)$ in the ratio $3 : 4$, find the coordinates of $B$.
Step-by-Step Solution
Key Concept: $-1 = \dfrac{3x + 4(2)}{7} \Rightarrow 3x + 8 = -7 \Rightarrow 3x = -15 \Rightarrow x = -5$. $2 = \dfrac{3y + 4(5)}{7} \Rightarrow 3y + 20 = 14 \Rightarrow 3y = -6 \Rightarrow y = -2$. $B(-5, -2)$.
$\dfrac{3x + 8}{7} = -1 \Rightarrow 3x = -15 \Rightarrow x = -5$. [1.0 Mark]
$\dfrac{3y + 20}{7} = 2 \Rightarrow 3y = -6 \Rightarrow y = -2$. Point $B$ is $(-5, -2)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $x = -5$: 1.0 Mark
Solving $y = -2 \Rightarrow B(-5, -2)$: 1.0 Mark
Correct Answer:
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