Question

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

Answer 1

Answer:

Midpoint of two points =(

2

x

1

+x

2

,

2

y

1

+y

2

)

Given, midpoint of (2a,4) and (−2,2b)=(1,2a+1)

=>(

2

2a−2

,

2

4+2b

)=(1,2a+1)

=>

2

2a−2

=1;

2

4+2b

=2a+1

=>2a−2=2

=>a=2

And,

2

4+2b

=2a+1

=>

2

4+2b

=2(2)+1=5

=>4+2b=10

=>2b=6

=>b=3

Answer 2

Answer:

  a = 2, b = 3.

Step-by-step explanation:

(check the attachment also)

Midpoint of (2a, 4) and (- 2, 2b) is (1, 2a + 1)

By using mid-point formula;

x  = (x1 + x2)/2

Or,1 = (2a – 2)/2           

Or,1 = a – 1

∴  a = 2

Also,

y  = (y1 + y2)/2

2a + 1 = ( 4 + 2b)/2

2a + 1 = 2 + b

∴  5 – 2 = b

∴   b = 3

Therefore,  a = 2, b = 3.

Hope this helps :))

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