# Rectangle Coordinates System

The line joining the points A(-3,5) and B(11,-5) cuts the line L : y = x at the point P and the x-axis at the point Q.

a) Find the coordinates of P and Q.

b) Hence, or otherwise, find the ratios AP : PQ : QB

### 1 Answer

Rating

- choyLv 51 decade agoFavorite Answer
a)

Eqn. of line AB:

(5 - -5)/(-3 - 11) = (y-5)/(x - -3)

-10/14 = (y-5)/(x + 3)

14(y-5)= -10(x + 3)

14y - 70 = -10x - 30

10x + 14y - 40 = 0

5x + 7y - 20 = 0 -------(1)

Put x=y into (1),

5y + 7y - 20 = 0

12y = 20

y = 5/3

x = y = 5/3

P is (5/3 , 5/3)

Put y=0 into (1),

5x + 7 x 0 - 20 = 0

5x = 20

x = 4

Q is (4 , 0)

b)

AP : PQ : QB

= (5/3 - -3) : (4 - 5/3) : (11 - 4)

= (5/3 + 3) : (4 - 5/3) : (11 - 4)

= 14/3 : 7/3 : 7

= 14 : 7 : 21

Still have questions? Get your answers by asking now.