Coordinate Geometry
RD Sharma
CBSE
Grade 10
Question:
If the point $P(2, 1)$ lies on the line segment joining $A(4, 2)$ and $B(8, 4)$, then:
(a) $AP = \dfrac{1}{2} AB$
(b) $AP = \dfrac{1}{3} AB$
(c) $AP = \dfrac{1}{4} AB$
(d) $AP = 2 AB$
Step-by-Step Solution
Key Concept: For $P(6,3)$, $AP = \sqrt{(6-4)^2 + (3-2)^2} = \sqrt{5}$. $AB = \sqrt{(8-4)^2 + (4-2)^2} = 2\sqrt{5}$. Thus $AP = \dfrac{1}{2} AB$.
$AP = \sqrt{5}$ and $AB = 2\sqrt{5} \Rightarrow AP = \dfrac{1}{2} AB$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating $AP/AB = 1/2$: 1.0 Mark
Correct Answer: $AP = \dfrac{1}{2} AB$
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