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Reflection of the midpoint of the line segment joining the points 1,2 and  3,4 with respect to the line y=x  is a,b . The value of a+b is

a
2
b
3
c
4
d
5

detailed solution

Correct option is D

Suppose that the midpoint of the line segment joining the points (1,2) and (3,4) is PHence, P=x1+x22,y1+y22=1+32,2+42=2,3 The image of the point Px1,y1 in the line y=x is y1,x1 Therefore, the image of the point P(2,3) in the line y=x is (a,b)=(3,2) It implies that a+b=3+2=5

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