# Find the other endpoint of a segment, with the endpoint (-1,9) and the midpoint (-9,-10).

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Given the endpoint is A(-1,9) and the midpoint is M(-9,-10).

We need to find the coordinates of the other endpoint of the line segment AB.

Then we will assume that the other endpoint is B(Bx, By).

Then we will use the midpoint formula to find the endpoint.

We know that:

Mx = (Ax + Bx)/2

==> -9 = (-1+ Bx)/2

==> -18 = -1 + Bx

==> Bx = -18 + 1= -17

==> Bx = -17.

My = (Ay+By)/2

==> -10 = (9+By)/2

==> -20 = 9 + By

==> By = -20 -9 = -29

==> By = -29.

**Then, the other endpoint B is ( -17. -29).**

The midpoint of two points (x1, y1) and (x2, y2) is given by [(x1+x2)/2 , (y1+ y2)/2]

Now we are given the midpoint as (-9,-10) and one of the end points as (-1,9).

Let teh point we need to find be (X , Y)

Therefore (X -1) / 2 = -9

=> X - 1 = -18

**=> X = -17**

Also, (Y + 9)/2 = -10

=> Y + 9 = -29

**=> Y = -29**

**Therefore the other end point is (-17 , -29)**

We'll write the formula of the midpoint, whose endpoints are (x1,y1) and (x2,y2):

xM = (x1 + x2)/2

yM = (y1 + y2)/2

We'll put x1 = -1 and y1 = 9, xM = -9 , yM = -10.

-9 = (-1+x2)/2

We'll multiply by 2:

-18 = x2 - 1

**x2 = -17**

-10 = (9 + y2)/2

We'll multiply by 2:

-20 = y2 + 9

**y2 = -29**

**The coordinates of the other endpoint are: (-17 , -29).**