MCQ
The distance between the points $(m, - n)$ and $(-m, n)$ is :
- A$\sqrt{\text{m}^2+\text{n}^2}$
- B$\text{m + n}$
- ✓$2\sqrt{\text{m}^2+\text{n}^2}$
- D$\sqrt{2\text{m}^2+\text{n}^2}$
✓
Answer
Correct option: C.
$2\sqrt{\text{m}^2+\text{n}^2}$
The distance between two points is given by
$\text{d}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$\text{d}=\sqrt{(-\text{m}-\text{m})^2+(\text{n}-\text{(-n)})^2}$
$=\sqrt{(-2\text{m})^2+(2\text{n})^2}$
$=\sqrt{4\text{m}^2+4\text{n}^2}$
$=\sqrt{4(\text{m}^2+\text{n}^2)}$
$\text{d}=2\sqrt{\text{m}^2+\text{n}^2}$
$\text{d}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$\text{d}=\sqrt{(-\text{m}-\text{m})^2+(\text{n}-\text{(-n)})^2}$
$=\sqrt{(-2\text{m})^2+(2\text{n})^2}$
$=\sqrt{4\text{m}^2+4\text{n}^2}$
$=\sqrt{4(\text{m}^2+\text{n}^2)}$
$\text{d}=2\sqrt{\text{m}^2+\text{n}^2}$
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