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let x1,x2,x3,y1,y2,y3,z1,z2,z3 be three points.x1,x2,x3,y1,y2,y3,z1,z2,z3 are in gp with same ratio r then x1,y1,z1,x2,y2,z2,x3,y3,z3 are in................................

let x1,x2,x3,y1,y2,y3,z1,z2,z3 be three points.x1,x2,x3,y1,y2,y3,z1,z2,z3 are in gp with same ratio r then x1,y1,z1,x2,y2,z2,x3,y3,z3 are in................................
 

Grade:Select Grade

1 Answers

Vikas TU
14149 Points
3 years ago

We have (y2-y1)/(x2-x1) = (y3-y2)/(x3-x1)=(y3-y1)/(x3-x1) = m (slope of the line, so

(y2-y1) = m(x2-x1), dividing by x1x2 and rearranging, we get (y1-y2)/x1x2 = m(1/x2 -1/x1) …… (1)

Similarly (y2-y3)/x2x3 = m(1/x3–1/x2) and …., (2)

(y3-y1)/x3x1 = m(1/x1 –1/x2) …… (3)

(1)+(2)+(3) gives RHS =0, so LHS =0

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