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