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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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