Question

The distance of the point $P=(-6,8)$ from the origin is

• A. $8$
• B. $2\sqrt{7}$
• C. $10$
• D. $6$

Answer 1

The correct option is C

$10$

Explanation of Distance of the point.

The explanation for the correct option:

The center of the coordinate system is called the origin. The axes intersect when both $x$ and $y$ are zero. The coordinates of the origin are $(0,0)$.

The formula of distance: $\mathbf{Distance}\mathbf{=}\mathbf{}\sqrt{{\mathbf{(}{\mathbf{x}}_{\mathbf{2}}\mathbf{-}{\mathbf{x}}_{\mathbf{1}}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}{\mathbf{y}}_{\mathbf{2}}\mathbf{-}{\mathbf{y}}_{\mathbf{1}}\mathbf{)}}^{\mathbf{2}}}$

$\mathrm{P}=(-6,8)=(x_1,y_1)$

origin:$(0,0)=(x_2,y_2)or(x,y)$

Calculate the distance:

$$\begin{gathered} \mathrm{Distance}=\sqrt{{(0-(-6\left)\right)}^2+{(0-8)}^2} \\ =\sqrt{{\left(6\right)}^2+{(-8)}^2} \\ =\sqrt{36+64} \\ =\sqrt{100} \\ =10\mathrm{unit} \end{gathered}$$

So, the distance of the point $(-6,8)$ from the origin is $\mathbf{“}\mathbf{10}\mathbf{}\mathbf{unit}\mathbf{”}$.

Hence, the correct choice is “Option C”.