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Solution for 11

ax+by + c = 0                        dx+ey + f = 0

by = -ax -c                              ey = -dx -f

y = -(a/b)x – c/b                    y = -(d/e)x – f/e

When 2 lines are parallel, their gradients are equal,

so   -(a/b) = -(d/e)    =>  (a/b) = (d/e)   (proven)

 

Solution for 16

A = (1, 2)

B = (6,7)

AP : BP  = 2 : 3

The coordinates of the point P(x, y) which divides the line segment joining the points A (x₁, y₁) and B(x₂, y₂), internally, in the ratio m₁ : m₂ is given by the section formula:

P (x, y) = [(mx₂ + nx₁)/ (m + n) , (my₂ + ny₁)/(m + n) ]

              = {  [(2×6) + (3×1)]  / (2+3) ,  { [(2×7) + (3×2)] / (2+3) }

              = [ (12+3) / 5 ,  (14+6) / 5 ]

               = [ 15/5 , 20/5]

               =(3 , 4)

Hence the coordinates of P is (3 , 4).

1 Reply 1 Like ✔Accepted Answer

thanks very much.

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