Let `P(x_1, y_1)` be a point a line an let `ax+by+c=0`.lf `L(h, k)` is the foot of perpendicular drawn from `P` on this line and `Q (alpha,beta)` is the image of `P` in the given line the prove that

Let P(x_1,y_1) be a point and let ax + by +c =0 be a line. If L (h, k) is the foot of perpendicular drawn from P on this line and Q (alpha, beta) is the image of P in the given line, then prove that : (h-x_1)/a=(k-y_1)/b=-((ax_1+by_1+c)/(a^2+b^2)) .

Let P (x_1,y_1) be a point and let ax + by+ c = 0 be a line. If L (h, k) is the foot of perpendicular drawn from P on this line and Q (alpha, beta) is the image of P in the given line, then prove that

The foot of the perpendicular from (0,0) to the line x cos alpha+y sin alpha=p is

The foot of the perpendicular from (0, 0) to the line x cos alpha+y sin alpha=p is

If Q(h,k) is the foot of the perpendicular from P(x_(1) ,y_(1)) on the line ax + by+ c=0 then Q(h,k) is

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

P is a point on the straight line 7x-4y-29=0 . If the foot of the perpendicular drawn from P on the line 5x+2y+18=0 be N(-2,-4) , find the coordinates of P.