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Question
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
Solution
It is given that mid-point of line segment joining A(x , y + 1 ) and B(x + 1 , y + 2 ) is C`(3/2,5/2)`
In general to find the mid-point P(x , y) of two points `A(x_1 , y_1)` and `B (x_2 , y_ 2)` we use section formula as,
`P( x , y) = (( x_1 + x_2) / 2 , ( y _1 + y_2) /2)`
So,
`(3/2 , 5/2) =((2x + 1 ) / 2 , (2y + 3 ) /2 )`
Now equate the components separately to get,
`(2x +1)/2 = 3/2`
So,
x = 1
Similarly,
`(2y + 3)/2=5/2`
So,
y = 1
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