Question

The coordinates of point T are (10,18) and the midpoint of bar (ST) is (5,8). What are the coordinates of point S.

Answer 1

The coordinates of point S, given the midpoint of ST and the coordinates of point T, are (0, -2). This is determined by using the midpoint formula and solving for the unknown endpoint's coordinates.

Step-by-step explanation:

To find the coordinates of point S given the coordinates of point T (10,18) and the midpoint of ST (5,8), recall that the coordinates of the midpoint M of a segment with endpoints (x1, y1) and (x2, y2) are given by M = ((x1+x2)/2, (y1+y2)/2). In this case, we have the midpoint's coordinates, so we need to solve for the unknown endpoint's coordinates (coordinates of S).

Let's denote the coordinates of S as (x, y). We can set up the following equations using the midpoint formula:

(x + 10)/2 = 5

(y + 18)/2 = 8

By solving these equations, we find that:

x = 2(5) - 10 = 0
= 2(8) - 18 = -2

Therefore, the coordinates of point S are (0, -2).