Question content area top

Part 1
The coordinates of point T are ​(0​,2​). The midpoint of ST overbar is ​(1​,negative 5​). Find the coordinates of point S.
Question content area bottom
Part 1
The other endpoint is
  
enter your response here.
​(Type an ordered​ pair.)

1 answer

To find the coordinates of point \( S \), given that point \( T \) has coordinates \( (0, 2) \) and the midpoint \( M \) of segment \( \overline{ST} \) is \( (1, -5) \), we can use the midpoint formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Here, \( M \) is the midpoint, \( (x_1, y_1) \) is the coordinate of point \( S \), and \( (x_2, y_2) \) is the coordinate of point \( T \) which is \( (0, 2) \).

Let the coordinates of point \( S \) be \( (x, y) \). According to the midpoint formula:

\[ (1, -5) = \left( \frac{x + 0}{2}, \frac{y + 2}{2} \right) \]

We can set up two equations based on this:

  1. For the x-coordinates: \[ 1 = \frac{x + 0}{2} \implies 2 = x \implies x = 2 \]

  2. For the y-coordinates: \[ -5 = \frac{y + 2}{2} \implies -10 = y + 2 \implies y = -12 \]

Thus, the coordinates of point \( S \) are \( (2, -12) \).

The other endpoint is: \[ \boxed{(2, -12)} \]