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=((x_1+x_2)/(2),(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:

`(x_1+x_2)/(2)=-2`

substituting x1 and solving for x2:

`(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:

`(y_1+y_2)/(2)=-7`

we substitute y1 and solve for y2:

`(-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)