Find the coordinates of the foot of perpendicular drawn from the point (2,3) to the line 3x-4y+7=0?

1 Answer
Jan 22, 2018

Coordinates of the foot of the perpendicular

color(green)(B (47/25, 79/25))

Explanation:

enter image source here

To find the Slope of the line CD 3x - 4y + 7 = 0 Eqn (1)

y = (3/4)x + 7/4)

m = (3/4)

Slope of line AB perpendicular to the above line segment CD is

m1 = -1/m = -4/3

Equation of the perpendicular line AB passing through point (2,3) is

y - 3 = -(4/3) (x - 2)

3y + 4x = 17. Eqn (2)

Solving Eqns (1), (2) we get the foot of the perpendicular B drawn from A (2,3)

color(green)(B (47/25, 79/25))