Question

If a segment has one endpoint at A(-5, 1) and amidpoint at M(1,4), then what are thecoordinates of the other endpoint, B?

Answer 1

We have the following:

A(-5, 1)

M(1, 4)

B(x1, y1)

In order to first determine the point B, we do the following:

we first determine the lenght from the point A to the midpoint M:

`(1,\text{ 4)}-(-5,1)\Rightarrow(6,\text{ }3)`
`D_(AM)=\sqrt[]{(6)^2+(3)^2}^{}\Rightarrow D_(AM)=3\sqrt[]{5}`

From this, we do as follows:

*Fisrt we determine the form of the distance to that other point using our mid point or our start point A:

`(x,y)-(1,4)=(x-1,y-4)`

Or

`(x,y)-(-5,1)=(x+5,y-1)`

Where in our first case The distance should be 3sqrt(5).

From this, we can calculate that the point (7, 7) will be our B point. That can be seen as follows:

`(7-1,7-4)=(6,3)`

Since the vector that is formed from the vector B to the midpoint is the same as the vector formed from the midpoint to A.

And the distance of both is double the distance from A to M.