MCQ
The distance between the points $P(-6, 8)$ from the origin is :
- A$8$
- B$2\sqrt{7}$
- ✓$10$
- D$6$
✓
Answer
Correct option: C.
$10$
$\therefore$ Distance between the points $\left(\mathrm{x}_1, \mathrm{y}_2\right)$ and $\left(\mathrm{x}_2, \mathrm{y}_2\right)$
$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}$
Here, $x_1=-6, y_1=8$ and $x_2=0, y_2=0$
$\therefore$ Distance between $P(-6,8)$ and origin i.e. $,O(0,0)$
$\text{PO}=\sqrt{[0-(-6)]^2+(0-8)^2}$
$\text{PO}=\sqrt{(6)^2+(-8)^2}$
$\text{PO}=\sqrt{36+64}$
$\text{PO}=\sqrt{100}$
$\text{PO}=10$
$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}$
Here, $x_1=-6, y_1=8$ and $x_2=0, y_2=0$
$\therefore$ Distance between $P(-6,8)$ and origin i.e. $,O(0,0)$
$\text{PO}=\sqrt{[0-(-6)]^2+(0-8)^2}$
$\text{PO}=\sqrt{(6)^2+(-8)^2}$
$\text{PO}=\sqrt{36+64}$
$\text{PO}=\sqrt{100}$
$\text{PO}=10$
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