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