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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
MCQ
If the distance between the points $A(4, p)$ and $B(1, 0)$ is $5$ then :
  • A
    $\text{p} = 4\text{ only}$
  • B
    $\text{p} = -4\text{ only}$
  • ✓
    $\text{p} = \pm4$
  • D
    $\text{p} = 0$
✓

Answer

Correct option: C.
$\text{p} = \pm4$
Using distance formula, we get
$\text{AB}=\sqrt{(4-1)^2+(\text{p}-0)^2}$
$\Rightarrow5=\sqrt{3^2+\text{p}^2}$
$\Rightarrow25=3^2+\text{p}^2$
$\Rightarrow25=9+\text{p}^2$
$\Rightarrow\text{p}^2=16$
$\Rightarrow\text{p}=\pm4$

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