Question

The coordinates of point T are ​(0​,3​). The midpoint of ST is ​(2​,−2​). Find the coordinates of point S. The other endpoint is nothing. ​(Type an ordered​ pair.)

Answer 1

Answer:

The coordinates of point S are (4,-7).

Step-by-step explanation:

Given the locations of points S and T, the midpoint coordinates are set by midpoint formulas:

$\bar x = \frac{x_{S}+x_{T}}{2}$ and $\bar y = \frac{y_{S}+y_{T}}{2}$

Where:

$x_{S}$, $x_{T}$ - x-Components of S and T.

$y_{S}$, $y_{T}$ - y-Components of S and T.

The coordinates of S are cleared:

$x_{S} = 2\cdot \bar x -x_{T}$

$y_{S} = 2\cdot \bar y - y_{T}$

If $\bar x = 2$, $\bar y = -2$, $x_{T} = 0$ and $y_{T} = 3$, the equations are now solved:

$x_{S} = 2\cdot (2) -0$

$x_{S} = 4$

$y_{S} = 2\cdot (-2)-3$

$y_{S} = -7$

The coordinates of point S are (4,-7).