Question

The coordinates of point t are given. The midpoint of ST is (5, -8) find the coordinates of point S

Answer 1

Let the co-ordinates of the point S be (x, y).

Let the co-ordinates of the point T be (a, b) (given values)

Let the midpoint of ST be O.

Then, O is (5, - 8)

Also, the midpoint of ST can be calculated as follows:

O is $(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )$

= $(\frac{x+a}{2}, \frac{y+b}{2} )$

Therefore,

$(\frac{x+a}{2} , \frac{y+b}{2} ) = (5, - 8)$

x = 10 - a and y = -16 - b

Hence the co-ordinates of S are (10 - a, -16 - b).