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Question

A straight line cuts the coordinate axes at A and B. If the midpoint of AB is (3,2), then find the equation of AB.

A
2x+3y12=0
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B
2x+3y+12=0
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C
2x+3y24=0
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D
None of these
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Solution

The correct option is B 2x+3y12=0
Let xintercept be a
yintercept be b

The coordinate of A is (a,0) and coordinate of B is (0,b)

Midpoint of AB=((x1+x2)2,(y1+y2)2)

(3,2)=(a+02,0+b2)

by comparing them

3=a2 2=b2

a=6b=4

Intercept form of line :

xa+yb=1

x6+y4=1

2x+3y12=1

2x+3y=12

2x+3y12=0

Hence, this is the answer.

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