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Question

The mid-point of the line segment joining (2a,4) and (2,2b) is (1,2a+1). Then the values of a and b respectively are


A

4 and 5

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B

3 and 5

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C

2 and 3

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D

1 and 2

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Solution

The correct option is C

2 and 3


Given that (1,2a+1) is the mid-point of (2a,4) and (2,2b).

We know that mid-point of the line joining two points A(x1,y1) and B(x2,y2) is given by (x1+x22,y1+y22)

2a22=1

2a=4

a=2
Also, 4+2b2=2a+1
4+2b=4a+2
2b=4a2
Since a=2, we have b=3
Hence, a=2 and b=3


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