Question

prove that the mid point of the line joining points (-5,12) and (-1,12) is a point of trisection of the line joining the points (-8,-5) and (7,10).​

Answer 1

Correct Question :--- Prove that the mid point of the line joining points (-5,12) and (-1,-12) is a point of trisection of the line joining the points (-8,-5) and (7,10).

Formula used :---

→ Mid - points of (x1,x2) and (y1,y2) = (x1+x2)/2 , (y1+y2)/2

→ If a (x,y) point divide the line (x1,x2) and (y1,y2) in ratio m1:m2 , than Point x = (m1*x2+m2*x1)/(m1 + m2) and

y = (m1*y2+m2*y1)/(m1 + m2)

→ Point of Trisection means in ratio 1:2 .....

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Solution :---

→ mid point of the line joining points (-5,12) and (-1,-12) =

= (-5-1)/2 = -6/2 = (-3)

= (12-12)/2 = 0/2 = 0

Hence, Mid - Point of line will be (-3,0) .

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Now, lets check trisection points of (-8,-5) ans (7,10)

Here , m1 = 1 , m2 = 2

→ x = [ 1*7 + 2*(-8) ] / [ 1+2 ] = [ 7 -16 ] /3 = (-9)/3 = (-3)

→ y = [ 1*10 + 2*(-5) ] / [ 1+2 ] = [ 10 - 10] /3 = 0/3 = 0

Points of Tri-section are (-3,0) .

✪✪ Hence Proved ✪✪

Hence, we can say that , the mid point of the line joining points (-5,12) and (-1,-12) is a point of trisection of the line joining the points (-8,-5) and (7,10).