SATHEE: Straight Line Question 286

Straight Line Question 286

Question: If the coordinates of the points A, B, C, D, be $ (a,\ b), $ $ ({a}’,\ {b}’), $ $ (-a,\ b) $ and $ ({a}’,\ -{b}’) $ respectively, then the equation of the line bisecting the line segments AB and CD is

Options:

A) $ 2{a}‘y-2bx=ab-{a}’{b}’ $

B) $ 2ay-2{b}’\ x=ab-{a}’{b}’ $

C) $ 2ay-2{b}‘x={a}‘b-a{b}’ $

D)None of these

Show Answer

Answer:

Correct Answer: B

Solution:

Mid point of $ AB=E( \frac{a+{a}’}{2},\frac{b+{b}’}{2} ) $ and mid point of $ CD=F( \frac{{a}’-a}{2},\frac{b-{b}’}{2} ) $ . Hence equation of line EF is $ y-\frac{b+{b}’}{2} $ $ =\frac{b-{b}’-b-{b}’}{{a}’-a-a-a’}( x-\frac{a+{a}’}{2} ) $ On simplification, we get $ 2ay-2{b}‘x-=ab-{a}’{b}’ $ .

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Straight Line Question 286

Question: If the coordinates of the points A, B, C, D, be $ (a,\ b), $ $ ({a}’,\ {b}’), $ $ (-a,\ b) $ and $ ({a}’,\ -{b}’) $ respectively, then the equation of the line bisecting the line segments AB and CD is

Options:

Answer:

Solution:

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