Question

The co-ordinates of the points P and Q are (3, y) and (x, 5), and the co-ordinates of the mid-point of line segment PQ are (2, 4). Find the values of x and y.

Answer 1

The midpoint formula gives the midpoint:

`((x1 + x2)/2, (y1 + y2)/2)`

For P(3, y) and Q(x, 5),

The midpoint is `((3 + x)/2, (y + 5)/2)`, which equals (2, 4),

So,

`(3 + x)/2` = 2

3 + x = 4

∴ x = 1

`(y + 5)/2` = 4

y + 5 = 8

∴ y = 3

Hence x = 1 and y = 3.