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Question

Write down the equation of the line whose gradient is 32 and which passes through P, where P divides the line segment joining A(2,6) and B(3,4) in the ratio 2:3

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Solution

A=(2,6) B=(3,4)

P divides AB in 2:3 ratio

x=mx2+nx1m+ny=my2+ny1m+n


x=2(3)+3(2)2+3y=2(4)+3(6)2+3

x=0 y=2

P(0,2)m=32

(yy1)=m(xx1)

(y2)=32(x0)

2y4=3x

3x2y+4=0.

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