Question

The line segment connecting `(x_1, 6) and (9, y_2)` is bisected by the point (7, 3) . What are the values of `x_1 and y_2`?

Answer 1

`x_1=5` and `y_2=0`

Explanation:

Mid-point of a line segment connecting `(x_1,y_1)` and `(x_2,y_2)` is `((x_1+x_2)/2,(y_1+y_2)/2)`

We are given points `(x_1,6)` and `(9,y_2)` and therefore their midpoint is `((x_1+9)/2,(6+y_2)/2)` and as it is `(7,3)`, we have

`(x_1+9)/2=7` or `x_1+9=14` or `x_1=14-9=5`

and `(6+y_2)/2=3` or `6+y_2=6` or `y_2=0`