A(-5,2),B(- 1,7)
KAB=5/4
So k =-4/5.
The coordinate of the midpoint of AB is (-3,5/2).
So the perpendicular equation of AB is: y-5/2=-4/5(x+3), that is, y =-4/5x+110.
When x=0, y =110.
When y=0, X= 1/8.
That is, the coordinates of point P are (0,110) and (1/8,0). According to the known two points, the linear equation passing through these two points is obtained, that is, 2 =-5k+b.
7=-k+b gives k=5/4 b=33/4.
That is, the equation is y=5/4*x+33/4.
If the distance between these two points is equal, we can know that any point on the middle vertical line of the lane change is equal to the distance between these two points. If we assume that x=0 and y=0 on the coordinate axis, we can get the corresponding coordinates.
The slope of two straight lines is multiplied by-1, and the slope of that straight line is -4/5, that is, y=-4/5x+b (1).
Because the straight line passes through the midpoint of the known straight line, y=5/2 x=-3 is substituted into the formula (1), and b =110.
The equation is y =-4/5 * x+110 (2).
Let x=0 be substituted into formula (2) and y =110, that is, (0,110).
Let y=0 be substituted into formula (2) to get x = 1/8 (1/8,0), that is, the coordinates of point p are (0,110) and (1/8,0).