MCQ
The distance between the points $(a, a)$ and $(-\sqrt{3} a, \sqrt{3} a)$ is
- A$2 \sqrt{2}$ units
- B$3 \sqrt{2} a$ units
- C2 units
- ✓$2 a \sqrt{2}$ units
✓
Answer
Correct option: D.
$2 a \sqrt{2}$ units
Let the points be $A (a, a)$ and $B (-\sqrt{3} a, \sqrt{3} a)$
$\therefore AB=\sqrt{(-\sqrt{3} a-a)^2+(\sqrt{3} a-a)^2}$
$=\sqrt{3 a^2+a^2+2 \sqrt{3} aa+3 a^2+a^2-2 \sqrt{3} aa}$
$=\sqrt{6 a^2+2 a^2}$
$=\sqrt{8 a^2}$
$=2 a \sqrt{2} \text { units }$
$\therefore AB=\sqrt{(-\sqrt{3} a-a)^2+(\sqrt{3} a-a)^2}$
$=\sqrt{3 a^2+a^2+2 \sqrt{3} aa+3 a^2+a^2-2 \sqrt{3} aa}$
$=\sqrt{6 a^2+2 a^2}$
$=\sqrt{8 a^2}$
$=2 a \sqrt{2} \text { units }$
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