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).

Answer 1

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