PROOF OF MY CENTRAL POINT THEORY

FUNDAMENTAL PROOF OF THE CENTRAL POINT AND ITS SLOPE

At central point (x_g, y_g) in the ordered pair (X, Y) of straight line equation Ax+By=C, the formula for x_g and y_g  are given as;

X_g = C/2A

Y_g = C/2B

PROOF!

Given Ax+By=C, the central pair can proved by equally pairing x to y.

i.e   Ax = C-By………(1)

       

       By = C-Ax……(2)

Equating Ax in equation(1) to C-Ax in equation (2), we have

X_g = C/2A

Also, equating By in equation(2) to C-By in equation (1), we have

y_g = C/2B

THE SLOPE

At central point, the slope of straight line equation Ax+By=C is given as m = -y_g/x_g where x_g and y_g denoted as central point pairs and m denoted as slope.

 PROOF!

 Given Ax+By=C, the slope of the straight line can be determined by moving term Ax to right hand side and divide both side by the constant B

Y = -(A/B)x + C/B

But let m=-A/B(slope) and b=C/B(intercept), hence we have

Y = mx+b……..(1)

Equally pairing m to y, we have

Y = mx+b…….(2)

-mx = b-y……(3)

Equating y in eqn(2) to b-y in eqn(3), we have

Y = b………(4)

Also, equating –mx in eqn(3) to mx+b in eqn(2), we have

M =-b/2x……..(5)

Putting eqn(4) into eqn(6), we have

M= -y/x  or  m= -y_g/x_g:  hence proved!





REFERENCE
*Adongo Ayine William(Me), Transcript(2008), Posted(EMS-Bolga Branch) to Mathematical Association of Ghana (Tittle: New Mathematical Concept.....) in the Year 2008.