Question

The coordinates of point T are (0,6). The midpoint of ST is (4.-6). Find the coordinates

Answer 1

Answer:

The coordinates of endpoint S are $S(x,y) = (8,-18)$.

Step-by-step explanation:

Let $T(x, y) = (0, 6)$ and $M(x,y) = (4,-6)$, which is the midpoint of line segment ST. From Linear Algebra we get that midpoint is the following vector sum of endpoints S and T. That is:

$M(x,y) = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot T(x,y)$ (Eq. 1)

Now clear S in the previous expression:

$S(x,y) = 2\cdot M(x,y) - T(x,y)$ (Eq. 1b)

Then, the coordinates of point S are:

$S(x,y) = 2\cdot (4,-6) - (0,6)$

$S(x,y) = (8, -18)$

The coordinates of endpoint S are $S(x,y) = (8,-18)$.