three points p(h,k) q(x1,y1) and r(x2,y2) lie on a line. show that (h-x1) (y2-y1)= (k-y1) (x2-x1)

Dear student
Since the points P,Q and R lie on a line i.e, are collinear, therefore,Slope of PQ=Slope of QRy1-kx1-h=y2-y1x2-x1k-y1h-x1=y2-y1x2-x1Cross multiplying, we haveh-x1y2-y1=k-y1x2-x1
Regards

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If a(x1,y1),b(x2,y2),c(x3,y3) are collinear then slope of ab=slope of bc
​i.e. y2-y1/x2-x1=y3-y2/x3-x2
p,q,r are collinear then
k-y1/h-x1=y2-y1/x2-x1
(h-x1)(y2-y1)=(k-y1)(x2-x1)
Hence Proved


 
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Rohit Jains ans is lit follow his
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