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.

Answer 1

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