# Rectangle Coordinates System

Given the points A(-1,3) and B(5,-8).

P is a point on the line segment AB such that AP : PB = r : 1.

a) Find the coordinates of P in terms of r.

b) Hence, find the ratio in which the line x - 2y - 5 = 0 divides the line segment AB

### 1 Answer

Rating

- choyLv 51 decade agoFavorite Answer
a)

let P be (x,y)

x = (1(-1) + r(5))/(1 + r) = (5r - 1)/(1 + r)

y = (1(3) + r(-8))/(1 + r) = (3 - 8r)/(1 + r)

ans: P is ((5r - 1)/(1 + r) , (3 - 8r)/(1 + r))

b)

assume line AB and the line x - 2y - 5 = 0 intercept at P

Put P into the eqn., we have

(5r - 1)/(1 + r) - 2(3 - 8r)/(1 + r) - 5 = 0

(5r - 1) - 2(3 - 8r) - 5(1 + r) = 0

5r - 1 - 6 + 16r - 5 - 5r = 0

16r = 12

r = 12/16 = 3/4

AP : PB = r : 1 = 3/4 : 1 = 3 : 4

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