Question

The distance of the point $(\alpha ,\beta )$ from the origin is

• A. $\alpha .\beta$
• B. ${\alpha }^2.{\beta }^2$
• C. $\sqrt{{\alpha }^2-{\beta }^2}$
• D. $\sqrt{{\alpha }^2+{\beta }^2}$

Answer 1

The correct option is D

$\sqrt{{\alpha }^2+{\beta }^2}$

Determine the distance.

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: $\mathrm{Distance}=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Need to find the distance between the point$(\alpha ,\beta )=(x_1,y_1)$ and origin $(0,0)=(x_2,y_2)or(x,y)$

Use the distance formula to calculate the distance:

$$\begin{gathered} Dis\tan ce=\sqrt{{(0-\alpha )}^2+{(0-\beta )}^2} \\ =\sqrt{{(0-\alpha )}^2+{(0-\beta )}^2} \\ =\sqrt{{\alpha }^2+{\beta }^2} \end{gathered}$$

The distance of the point $(\alpha ,\beta )$ from the origin is $\sqrt{{\mathit{\alpha }}^{\mathit{2}}\mathit{+}\mathit{}{\mathit{\beta }}^{\mathit{2}}}$.

Hence, the correct choice is “Option D”.

The explanation for the incorrect option:

Since the distance is $\sqrt{{\mathit{\alpha }}^{\mathit{2}}\mathit{+}\mathit{}{\mathit{\beta }}^{\mathit{2}}}$ as calculated above which is not equivalent to the values mentioned in Option A, Option B, and Option C.
Hence, Option A, Option B, and Option C. are incorrect options.

Hence, the correct option is “Option D”.