The distance of the point $ \mathrm{P}(-6,8) $ from the origin is
(A) 8
(B) $ 2 \sqrt{7} $
(C) 10
(D) 6

Given: 

A point $P( -6,\ 8)$.

To do: 

We have to find its distance from the origin.

Solution:

Given point is $P( -6,\ 8)$.

We know that, 

If there two points $( {x_{1},\ y_{1})\ and\ ( x_2},\ y_{2})$, then

The distance between the two points $=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Here, $x_{1}=-6,\ y_{1}=8,\ x_{2}=0\ and\ y_{2}=0$,

On substituting these value in formula,

Distance from the origin $=\sqrt{( 0-( -6))^{2}+(0-( 8))^{2}}$

$=\sqrt{( 6)^{2}+( -8)^{2}}$

$=\sqrt{36+64}$

$=\sqrt{100}$

$=\pm10$

Since, distance can't be negative, therefore we reject the value $x=-10$.

$\therefore$ Distance of the point $P( -6,\ 8)$ is $10$ unit.

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Updated on: 10-Oct-2022

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