Question

The distance between the points $A(0,6)$ and $B(0,-2)$ is

• A. $6$
• B. $8$
• C. $4$
• D. $2$

Answer 1

The correct option is B

$8$

Determine the distance between the points $A(0,6)$ and $B(0,-2)$.

The explanation for the correct option:

Given point are,

$$\begin{gathered} A(x_1,y_1)=(0,6) \\ B(x_2,y_2)=(0,-2) \end{gathered}$$

Use the distance formula to calculate the distance:

$$\begin{gathered} D=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2} \\ =\sqrt{(0-0{)}^2+(-2-6{)}^2} \\ =\sqrt{(0{)}^2+(-8{)}^2} \\ =\sqrt{0+64} \\ =\sqrt{64} \\ =8 \end{gathered}$$

The distance between the points, $8$ i.e. equivalent to Option B.

The explanation for the incorrect option:

Since the distance between the points is $8$ i.e. calculated above is not equivalent to the values mentioned in Option A, Option C, and Option D.
Hence, Option A, Option C, and Option D. are incorrect options.

Hence, the correct option is Option B.