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

Question

8824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-22T12:50:13

Coordinates of the foot of the perpendicular

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

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))#