Question

If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.

Answer 1

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