The coordinates of points T are (0,5). The midpoint of ST is (6,-7). Find the coordinates of point S

Answer 1

Draw a quick sketch (you can do this on a grid if you like, but just a straight line with the coordinates will also work.

1. T (0,5) ----------------------------------- S (6, -7) also note, it's 6 units (x) to the midpoint, so it will be 6 units beyond 6 (making it 12 for x); same idea for y (it's 12 units to y midpoint, so 12 units beyond would be -19)
2. given the midpoint, use the midpoint formula to solve for S: (x + x₁)/2 , (y + y₁)/2
3. (0 + x)/2 = 6 (for the x value of point S); multiply both sides by 2; x = 12
4. (5 + y)/2 = -7 (for the y value of point S); multiply both sides by 2, then subtract 5; y = -19
5. coordinates for point S (12, -19)

Answer 2

Answer 3

Let S(x,y). Then (x + 0)/2 = 6, x = 12. (y + 5)/2 = -7, y = -19. S(12, -19)