Question

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

Answer 1

Hey Pretty Stranger!

The Distance between 2 points $\sf\:(x_{1}, y_{1})\: and \sf\:(x_{2}, y_{2})$ is given by :

$\boxed{ \red{\sf \: d = \sqrt{ ({x_{2} - x_{1}})^{2} + ({y_{2} - y_{1}})^{2} }}}$

Where, $\sf\: x_{1} = 0, y_{1} = 6\: and\: x_{2} = 0, y_{2} = -2$

So, Distance between A(0,6) and B(0,-2) :

$\sf \: AB = \sqrt{ ({0 - 0})^{2} + ({ - 2 - 6})^{2} }$

$\longrightarrow \sf \: \sqrt{ {(0 - 0)}^{2} + ( { - 2 - 6})^{2} }$

$\longrightarrow \sf \: \sqrt{0 + ({ - 8})^{2} }$

$\longrightarrow \sf \: \sqrt{ {8}^{2} }$

$\longrightarrow \sf \: \sqrt{64}$

$\longrightarrow \sf \: 8$

$\therefore$ Distance between the points A(0, 6) and B(0, -2) is 8.

Answer 2

Given ,

The two points are

• A(0 , 6) and
• B(0 , -2)

We know that , the distance between two points is given by

$\sf \fbox{ Distance = \sqrt{ ({x_{2} - x_{1}})^{2} + ({y_{2} - y_{1}})^{2} \: } \: \: }$

Thus ,

$\sf \Rightarrow \sf \: D = \sqrt{ ({0 - 0})^{2} + ({ - 2 - 6})^{2} } \\ \\\sf \Rightarrow D = \sqrt{ {( - 8)}^{2} } \\ \\\sf \Rightarrow D = \sqrt{64} \\ \\\sf \Rightarrow D = 8 \: \: units$

$\therefore \sf \bold{ \underline{ The \: distance \: between \: the \: two \: points \: is \: 8 \: units}}$