Question

The point P is the foot of perpendicular from A(-5,7) to the line 2x-3y+18=0.
Determine:-
(i) the equation of the line AP
(ii) the coordinates of P

Answer 1

Heya User,

--> Slope of line given --> 2x - 3y + 18 = 0
=> 3y = 2x + 18
=> y = 2/3 ( x + 6 ) --> mx + c

--> Slope = m = 2/3
=> Slope of AP = -1 / ( 2/3 ) = -3 / 2 = -1.5
=> Equation of AP = 2y + 3x + 1 = 0

Given the two equations, we have the point AP as their common solution :-> P( -3 , 4 ) <--- Your Soln.

Answer 2

--> Slope of line given --> 2x - 3y + 18 = 0

=> 3y = 2x + 18

=> y = 2/3 (x + 6) --> mx + c

--> Slope = m = 2/3

=> Slope of AP = -1/(2/3) = -3/2 = -1.5 => Equation of AP = 2y + 3x + 1 = 0

Given the two equations, we have the point AP as their common solution :-> P(-3,

4) <--- Your Soln.