The perpendicular symbolic solution of a point outside a vector and a vector on two-dimensional plane

Establishing equations

Set a to a point outside the line,B,c to two points in a straight line

$\left\{\begin{matrix}

(X-ax,y-ay) \cdot (cx-bx,cy-by) =0 \

\FRAC{Y-CY}{X-CX}=\FRAC{Y-BY}{X-BX} \

\end{matrix} \right.$

?

Solve the symbolic solution

Using the Mathematics tool:

1. solve[{(x?-? Ax) * (CX?-? bx)? +? ( Y?-? ay) * (Cy?-? by)? = =???
2. ??? 0,? (y?-? Cy) * (x?-? bx)? = =? (y?-? by) * (x?-? cx)},? {x,?y}]??

Come to the following:

1. {{x?->?-(bx?-? cx)? ( Ax?bx?+?ay?by?-? ax?cx?-? ay?cy)?-? (-by?+???
2. ???????? CY)? (by?cx?-? Bx?cy)) /((BX?-? CX)? (-BX?+?CX)?-? (-by?+?cy) ^2)),???
3. ?? y?->?-(-ax?bx?by?-? ay?by^2?+?ax?by?cx?+?bx?by?cx?-? by?cx^2?+???
4. ???????? Ax?bx?cy?-? bx^2?cy?+?2?ay?by?cy?-? ax?cx?cy?+?bx?cx?cy?-???
5. ???????? ay?cy^2)/(bx^2?+?by^2?-? 2?bx?cx?+?cx^2?-? 2?by?cy?+?cy^2)}}??

You can then bring the above into the desired program, and obtain perpendicular.

Perpendicular symbolic solution of a point outside a vector on a two-dimensional plane and a vector