<PRE><B>Question 230539</B>
Three points have coordintes A(4,13), B(9,3) and C(10,8).
Find the equation of
(a) the line AB
Find the slope, m
m = diffy/diffx = 10/-5
m = -2
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Use either point to find b, then the eqn
y = mx+b to find b 
13 = -2*4 + b
b = 21
y = -2x + 21 (Eqn of AB)
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(b) the line through C perpendicular to the line y-4x=5.
y = 4x+5
m = -1/4 (slope perpendicular to m=4)
8 = -1/4*10 + b
b = 10.5
y = -(1/4)x + 10.5
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the line through C meets the line AB at point P.
Calculate the coordinates of P
y = -2x+21 = -x/4 + 10.5
1.75x = 10.5
x = 6
y = -12 + 21 = 9
P(6,9)
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and the ratio AP:PB
Since it&#39;s a straight, use the x values to get the ratio
A - 4
P - 6
B - 9
AP = 2
PB = 3
AP:PB = 2:3



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