1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Ratios Stage 6 - Year 11 Mathematic Extension 1 (Preliminary)

2 The coordinates of the point P(x,y) dividing the line in the ratio m:n are: f(x) x ● A(x 1,y 1 ) B(x 2,y 2 ) ● P(x,y) ● x1x1 xx2x2 x = mx 2 + nx 1 m + n y = my 2 + ny 1 m + n End of Slide m n

3 The coordinates of the point P(x,y) dividing the line in the ratio m:n are: x = mx 2 + nx 1 m + n y = my 2 + ny 1 m + n End of Slide f(x) x ● A(x 1,y 1 ) B(x 2,y 2 ) ● P(x,y) ● x1x1 xx2x2 m n P(x,y) divides AB in ratio m:n. Then = AP PB mnmn D AD = x – x 1 DC = x 2 – xPD||BC   = AP PB AD DC (The intercepts have equal ratios)  = mnmn x-x 1 x 2 -x m(x 2 -x) = n(x-x 1 ) mx 2 - mx = nx - nx 1 mx 2 + nx 1 = mx + nx mx 2 + nx 1 = x(m + n) mx 2 + nx 1 (m + n) x = Similarly for y.