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