Question

find the distanace of the point (1,2) from mid point of the line segment joining the points (6,8) and (5,1 )

Answer 1

First we have to get the mid point of the line segment having points ( 6 , 8 ) and ( 5 , 1 ). If we apply mid point formula,we can get the mid point of the line segment.

$Mid \: Point \: Formula =( \dfrac{ x_{1} + x_{2}}{2} , \dfrac{y_{1}+y_{2}}{2})$

Applying Mid Point Formula ,



$Mid \: \: point \: \: of \: \: line \: \: segment = ( \dfrac{ 6 + 5}{2} , \dfrac{8 +1 }{ 2} ) \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (\frac{11}{2} \: , \: \frac{9}{2} )$




Now ,we have to get the distance between the mid point of the line segment and ( 1 , 2 ). There is a formula which is used to measure the the distance between two points, distance formula.


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



$As \: \: the \: \: points \: \: are \: \: ( \dfrac{11}{2},\dfrac{9}{2} ) \: \: and \: \: ( 1 , 2 )$
$x_{1}= \dfrac{11}{2} \: \: \: \: \: x_{2} = 1 \\ \\ y_{1}= \dfrac{9}{2} \: \: \: \: \: \: \: y_{2} = 2$


Applying distance formula,


$Distance = \sqrt{ ( 1 - \dfrac{ 11}{2} )^{2} + (2 - \dfrac{9}{2}) {}^{2} } \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ \frac{81}{4} + \frac{25}{4} } \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ \frac{106}{4} } \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \sqrt{106} \: \: \: units$