Question

The midpoint of ST has coordinates (5,-8). Find the coordinate of point S when T (10,18)

Answer 1

The coordinates of point S are found using the midpoint formula given the midpoint (5, -8) and point T (10, 18), resulting in S being at (0, -34).

Step-by-step explanation:

To find the coordinates of point S given that the midpoint of segment ST is (5,-8) and point T is (10,18), we can use the midpoint formula which states that the midpoint M of a segment with endpoints S(x1, y1) and T(x2, y2) is given by M = ((x1+x2)/2, (y1+y2)/2). Since we know the coordinates of the midpoint M and point T, we can set up equations to solve for the x and y coordinates of point S.

The coordinates of the midpoint M are (5,-8), so we have:

1. (x1 + 10)/2 = 5
2. (y1 + 18)/2 = -8

Solving for x1 and y1 gives us:

1. x1 = 2*5 - 10 = 0
2. y1 = 2*(-8) - 18 = -34

Therefore, the coordinates of point S are (0, -34).

Answer 2