Equation of straight line AB:

Simplify:

Where, let the slopes of the straight line l 1 be k 1 and b 1+0, respectively, then:

The above formula can also be written in the form of Ax+By+C=0, namely:

According to the hypothesis, if d intersects with the straight line l 1, the point d can be expressed as (x4, k 1x4+b 1).

Let the straight line CD be l2, and according to the assumption that CD is perpendicular to AB, the reciprocal of the slope is l 1, and then take a negative value and substitute it into D to get the equation of the straight line l2:

Simplify:

According to the assumption that C crosses a straight line l2, point C can be expressed as (x3,-1/k1x3+(x4/k1+k1)).

It is not difficult to draw that the straight-line distance of CD ||| CD is the distance from C to straight line AB, namely:

Substitute k 1 and b 1 into the above formula, and the coordinates of A, B and C are known, so that the distance from point C to straight line AB can be obtained.

Referring to Baidu Encyclopedia, the formula of Ax+By+C=0 of straight line l 1 is substituted, which shows that the above derivation is correct.

To know where the straight line l 1 C(x3, y3) is, according to the inequality theorem, substitute x3 into the equation of the straight line l 1 and calculate the corresponding y. If y is greater than 0, it is proved to be on the upper right side, and if y is less than 0, it is proved to be on the lower left side.

Hope to adopt.