Question

The coordinates of midpoint M and endpoint C or a segment are M(-2,-7) and C(12,-9). Find the coordinates of the other endpoint15 )

Answer 1

we have that the midpoint is (-2,-7)

and the endpoint is (12,-9)

We remember the midpoint formula:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where (x1,y1) are the coordinates of one endpoint and

(x2,y2) are the coordinates for the other endpoint.

Here, we are trying to find (x2,y2) given that

(x1, y1) ---> (12, -9)

$\begin{gathered} x_1=12 \\ y_1=-9 \end{gathered}$

And since we also know the midpoint M(-2, -7), making a comparison with this and the midpoint formula, we get two equations, the first one is:

$\frac{x_1+x_2}{2}=-2$

substituting x1 and solving for x2:

$\frac{12+x_2}{2}=-2$$\begin{gathered} 12+x_2=4 \\ x_2=4-12 \\ x_2=-8 \end{gathered}$

And now, with the second equation which is:

$\frac{y_1+y_2}{2}=-7$

we substitute y1 and solve for y2:

$\frac{-9+y_2}{2}=-7_{}$

solving for y2:

$\begin{gathered} -9+y_2=-14_{} \\ y_2=-14+9 \\ y_2=-5 \end{gathered}$

This the other endpoint (x2,y2) is at (-8,-5)