# Calculate 6

Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].

Correct result:

d =  0.2

#### Solution:

$Ax=0; Ay=2 \ \\ Bx=9; By=5 \ \\ Cx=1; Cy=-1 \ \\ \ \\ l=\sqrt{ (Cx-Bx)^2+(Cy-By)^2 }=\sqrt{ (1-9)^2+((-1)-5)^2 }=10 \ \\ S_{2}=(Cy-By) \cdot \ Ax + (Cx-Bx) \cdot \ Ay + Cx \cdot \ By-Bx \cdot \ Cy=((-1)-5) \cdot \ 0 + (1-9) \cdot \ 2 + 1 \cdot \ 5-9 \cdot \ (-1)=-2 \ \\ d=|S_{2}| / l=|(-2)| / 10=\dfrac{ 1 }{ 5 }=0.2$

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