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Coordinate Geometry
NCERT Exemplar
CBSE
Grade 10

Question:

The coordinates of the point which divides the line segment joining $A(1, 3)$ and $B(4, 6)$ internally in the ratio $2 : 1$ are:
(a) $(3, 5)$
(b) $(5, 3)$
(c) $(2, 4)$
(d) $(4, 2)$

Step-by-Step Solution

Key Concept: Section formula: $x = \dfrac{m x_2 + n x_1}{m+n}, y = \dfrac{m y_2 + n y_1}{m+n}$.
$x = \dfrac{2(4) + 1(1)}{2 + 1} = \dfrac{8 + 1}{3} = 3$. [0.5 Mark]
$y = \dfrac{2(6) + 1(3)}{2 + 1} = \dfrac{12 + 3}{3} = 5$. Coordinates: $(3, 5)$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Applying section formula for $x = 3$: 0.5 Mark
Applying section formula for $y = 5$: 0.5 Mark

Correct Answer: $(3, 5)$
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