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MODEL PAPER 9 (STANDARD) — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMODEL PAPER 9 (STANDARD)1 Mark
MCQ
The distance between the points $(0, 0)$ and $(a - b, a + b)$ is
  • A
    $2 \sqrt{a b}$
  • ✓
    $\sqrt{2 a^2+2 b^2}$
  • C
    $2 \sqrt{a^2+b^2}$
  • D
    $\sqrt{2 a^2+a b}$
✓

Answer

Correct option: B.
$\sqrt{2 a^2+2 b^2}$
distance between the point. $(0,0)$ and $( a - b , a + b )$ is
$=\sqrt{(a-b-0)^2+(a+b-0)^2}$
$=\sqrt{(a-b)^2+(a+b)^2}$
$=\sqrt{a^2+b^2-2 a b+a^2+b^2+2 a b}$
$=\sqrt{2\left(a^2+b^2\right)}$
$=\sqrt{2 a^2+2 b^2} \text { units. }$

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