Coordinate Geometry
NCERT Exemplar
CBSE
Grade 10
Question:
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:
(a) $4$ only
(b) $\pm 4$
(c) $-4$ only
(d) $0$
Step-by-Step Solution
Key Concept: Use distance formula $\sqrt{(4-1)^2 + (p-0)^2} = 5$.
$\sqrt{3^2 + p^2} = 5 \Rightarrow 9 + p^2 = 25 \Rightarrow p^2 = 16 \Rightarrow p = \pm 4$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Distance equation setup $9 + p^2 = 25$: 0.5 Mark
Finding $p = \pm 4$: 0.5 Mark
Correct Answer: $\pm 4$
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