Question

The midpoint of a segment is (6,−6) and one endpoint is (13,−1). Find the coordinates of the other endpoint.

Answer 1

Answer:  The other endpoint of the segment is (-1, -11).

Step-by-step explanation:  Given that the midpoint of a line segment is (6, -6) and one endpoint is (13, -1).

We are to find the co-ordinates of the other endpoint.

Let (a, b) be the co-ordinates of the other end-point.

Then, according to the given information, we have

$\left(\dfrac{a+13}{2},\dfrac{b+(-1)}{2}\right)=(6,-6)\\\\\\\Rightarrow \left(\dfrac{a+13}{2},\dfrac{b-1}{2}\right)=(6,-6).$

Equating the x and y co-ordinates on both sides of the above, we get

$\dfrac{a+13}{2}=6\\\\\\\Rightarrow a+13=12\\\\\Rightarrow a=12-13\\\\\Rightarrow a=-1$

and

$\dfrac{b-1}{2}=-6\\\\\\\Rightarrow b-1=-12\\\\\Rightarrow b=-12+1\\\\\Righatrrow b=-11.$

Thus, the other endpoint of the segment is (-1, -11).

Answer 2

(-1, -11) 
13 is 7 away from 6, and -1 is 5 away from 6. Subtract 7 away from 6, and 5 away from -6.