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Question

# In the figure above, line ι (not shown) is perpendicular to segment AB and bisects segment AB. Which of the following points lies on line ι?

A
(0,2)
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B
(1,3)
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C
(3,1)
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D
(3,3)
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E
(3,6)
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Solution

## The correct option is D (3,3)Given line l bisects AB and perpendicular to AB.To find point lie on the line Slope of the line perpendicular to AB m1m2=−1−1m2=−1m2=1 And it will pass through the midpoint of AB Let coordinates of midpoint be (x,y)x=0+22=1y=0+22=1(x,y)=(1,1)So equation of line passing through (1,1) and having slope m=1(y−1)=1×(x−1)y−1=x−1y=x Hence (3,3) be the point that lie on this line.

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