SOLUTION: how can i find the cordinates of foot of the perpendicular in co-ordinate geometry?

Question 37332: how can i find the cordinates of foot of the perpendicular in co-ordinate geometry?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
how can i find the cordinates of foot of the perpendicular in co-ordinate geometry?IS IT PLANE C.G...OR 3D C.G?..LET ME TELL YOU FIRST FOR PLANE C.G.IF YOU NEED FOR 3D PLEASE COME BACK AND I SHALL EXPLAIN
LET US DO GENERAL AND SPECIFIC CASE WITH AN EXAMPLE.
LET US FIND THE FOOT OF THE PERPENDICULAR Q- SAY (H,K) FROM A POINT P (1,2)-SAY IN GENERAL (X1,Y1) ON TO A LINE L GIVEN BY EQN.X+Y=1..SAY IN GENERAL
AX+BY+C=0
SINCE Q IS THE FOOT OF PERPENDICULAR FROM P TO LINE L, IT LIES ON LINE L.HENCE
AH+BK+C=0.......................OR.........H+K=1 ....................I
PQ IS PERPENDICULAR TO L...SO PRODUCT OF SLOPE OF PQ AND SLOPE OF LINE L =-1
SLOPE OF PQ =(K-2)/(H-1)............OR..............(K-Y1)/(H-X1)
SLOPE OF LINE L =-1/1=-1..................OR...............-A/B
HENCE
{(K-2)/(H-1)}*(-1)=-1...........OR.....{(K-Y1)/(H-X1)}{-A/B}=-1
(K-2)/(H-1)=1...............OR.........(K-Y1)/(H-X1)=B/A
(K-2)=(H-1).................OR.........A(K-Y1)=B(H-X1)
K-2=H-1.......................OR.....AK-AY1=BH-BX1
H-K=-1...............OR...........BH-AK=BX1-AY1.....................II
NOW SOLVE EQNS.I AND II TO GET H,K....FOR THE NUMERICAL EXAMPLE WE GET
H+K+H-K=1-1=0
2H=0
H=0
0+K=1
K=1
HENCE THE FOOT OF PERPENDICULAR FROM P(1,2) TO THE LINE L ...X+Y=1
IS Q.(0,1)
RELATED QUESTIONS
Hello, I am stuggling with this co-ordinate geometry problem. Any help is greatly... (answered by ewatrrr)

Hi, can anyone help me figure out this co-ordinate geometry problem? I am having a tough... (answered by Gogonati)

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of... (answered by KMST)

I need your help on this question of circle from co-ordinate geometry, please help me .... (answered by richwmiller)

The point of intersection of co-ordinate axis... (answered by MathLover1)

How do you find the mid point of two... (answered by rapaljer)

Topic : Co-ordinate Geometry (Q) A line passes through the points with co-ordinates... (answered by mananth)

Hello, my son is having trouble with these Co-ordinate Geometry problems. I was never... (answered by scott8148)

Hi there tutors, I have a question that I don't know how to do. This is the equation :... (answered by KMST)