Coordinate Geometry
NCERT Exemplar Ch 07
CBSE_NCERT_EXEMPLAR_CH07
Grade 10
Question:
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:
$4$ only
$\pm 4$
$-4$ only
$0$
Step-by-Step Solution
Key Concept: Use distance formula $\sqrt{(4-1)^2 + (p-0)^2} = 5$.
Stepwise Solution:
$\sqrt{3^2 + p^2} = 5 \Rightarrow 9 + p^2 = 25 \Rightarrow p^2 = 16 \Rightarrow p = \pm 4$. [1.0 Mark]
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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