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=(CxBx)2+(CyBy)2=(19)2+((1)5)2=10 S2=(CyBy) Ax+(CxBx) Ay+Cx ByBx Cy=((1)5) 0+(19) 2+1 59 (1)=2 d=S2/l=(2)/10=15=0.2Ax=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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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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