# Center of line segment

Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is <0,1>.

Result

d =  4.472

#### Solution:

$t=(0+1)/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ \ \\ x_{0}=2-6 \cdot \ t=2-6 \cdot \ 0.5=-1 \ \\ y_{0}=1-4 \cdot \ t=1-4 \cdot \ 0.5=-1 \ \\ \ \\ x_{1}=1 \ \\ y_{1}=3 \ \\ d=\sqrt{ (x_{1}-x_{0})^2 + (y_{1}-y_{0})^2 }=\sqrt{ (1-(-1))^2 + (3-(-1))^2 } \doteq 2 \ \sqrt{ 5 } \doteq 4.4721 \doteq 4.472$

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