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Question
Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).
Solution
We have to find the distance of a point A (1, 2) from the mid-point of the line segment joining P (6, 8) and Q (2, 4).
In general to find the mid-point P(x,y) of any 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)`
Therefore mid-point B of line segment PQ can be written as,
`B(x,y) = ((6 + 2)/2, (4 + 8)/2)`
Now equate the individual terms to get,
x = 4
y = 6
So co-ordinates of B is (4, 6)
Therefore distance between A and B,
`AB = sqrt((4 - 1)^2 + (6 - 2)^2)`
`= sqrt(9 + 16)`
=5
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