One endpoint and the midpoint of a segment are given. Find the coordinates of the other endpoint. Show all your work.

A. Endpoint: (-1,9)
Midpoint: (-9,-10)
Endpoint: _______


B. Endpoint: (9,-10)
Midpoint: (4,8)
Endpoint: ________

A.(x,y), (-9,-10), (-1,9).

-9-x = 1/2(-1-x).
-18-2x = -1-x.
-x = 17.
X = -17.

-10-y = 1/2(9-y).
-20-2y = 9-y.
-y = 29.
Y = -29.

B. (x,y), (4,8), (9,-10).
4-x = 1/2(9-x).
Multiply both sides by 2, and Solve for x.

8-y = 1/2(-10-y).

For x,

-9 is 8 below -1
So, the other end is 8 below -9, or -17

Same for y.

The other problem is the same method.

To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Let's use this formula to solve the given problems:

A. Endpoint: (-1,9), Midpoint: (-9,-10)
Let the coordinates of the other endpoint be (x, y). Using the midpoint formula, we can write the equation:
(-9, -10) = ((-1 + x) / 2, (9 + y) / 2)

Simplifying this equation, we get:
-9 = (-1 + x) / 2 => Multiply both sides by 2
-18 = -1 + x => Add 1 to both sides
-17 = x

Substituting the value of x into the equation:
-10 = (9 + y) / 2 => Multiply both sides by 2
-20 = 9 + y => Subtract 9 from both sides
-29 = y

Therefore, the coordinates of the other endpoint are (-17, -29).

B. Endpoint: (9,-10), Midpoint: (4,8)
Let the coordinates of the other endpoint be (x, y). Using the midpoint formula, we can write the equation:
(4, 8) = ((9 + x) / 2, (-10 + y) / 2)

Simplifying this equation, we get:
4 = (9 + x) / 2 => Multiply both sides by 2
8 = 9 + x => Subtract 9 from both sides
-1 = x

Substituting the value of x into the equation:
8 = (-10 + y) / 2 => Multiply both sides by 2
16 = -10 + y => Add 10 to both sides
26 = y

Therefore, the coordinates of the other endpoint are (-1, 26).