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Question
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
Solution
It is given that mid-point of line segment joining A(6, 5) and B(4, y) is P(2, 6)
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,
`(2 , 6) = ((6 + 4)/2,(5 + y)/2)`
Now equate the y component to get,
`(5 + y) /2 = 6`
So,
y = 7
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