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CBSE Class 12-science Answered

Find the equation to the straight line which bisects the distance between the point AB and A'B' and also bisects the distance between the points (-A,B) and (A',-B')
Asked by kumarisakshi0209 | 24 Aug, 2019, 04:03: PM
answered-by-expert Expert Answer
Let the line L bisects the distance between the points (A, B) and (A', B')     
Also, L bisects the distance between the points (-A, B) and (A', -B')
Let P be the point of intersection of L and the line segment joining the points (A, B) and (A', B')
Therefore, the coordinates of P will be 

open parentheses fraction numerator A plus A apostrophe over denominator 2 end fraction comma fraction numerator B plus B apostrophe over denominator 2 end fraction close parentheses

Similarly, Q being the point of intersection of L and the line segment joing the points (-A, B) and (A', -B')
Therefore, coordinates of Q will be

open parentheses fraction numerator negative A plus A apostrophe over denominator 2 end fraction comma fraction numerator B minus B apostrophe over denominator 2 end fraction close parentheses

Therefore, L is the line joining P and Q

E q u a t i o n space o f space P Q thin space i s y minus fraction numerator B minus B apostrophe over denominator 2 end fraction equals fraction numerator fraction numerator B plus B apostrophe over denominator 2 end fraction minus fraction numerator B minus B apostrophe over denominator 2 end fraction over denominator fraction numerator A plus A apostrophe over denominator 2 end fraction minus fraction numerator negative A plus A apostrophe over denominator 2 end fraction end fraction open parentheses x minus fraction numerator negative A plus A apostrophe over denominator 2 end fraction close parentheses rightwards double arrow y minus fraction numerator B minus B apostrophe over denominator 2 end fraction equals fraction numerator B apostrophe over denominator A end fraction open parentheses x minus fraction numerator negative A plus A apostrophe over denominator 2 end fraction close parentheses 2 A y minus A B plus A B apostrophe equals 2 B apostrophe x plus B apostrophe A minus B apostrophe A apostrophe rightwards double arrow 2 A y minus 2 B apostrophe x equals A B minus A apostrophe B apostrophe equals 0
Answered by Renu Varma | 26 Aug, 2019, 11:59: AM

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