Given the coordinates of one endpoint of line segment AB and its midpoint M, find the coordinates of the other endpoint.

A(0,9), M(2,5)

Changes from A to M will be the same as the changes from M to B.

The x coordinate of B will be 2 + 2 = 4 and the y coordinate will be 5 - 4 = 1.

Write that as B(4,1)

The midpoint of

PQ
is
=M, 1−5
. One endpoint is
=P, −3−8
.
Find the coordinates of the other endpoint,
Q

To find the coordinates of the other endpoint of line segment AB, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are [(x1 + x2)/2, (y1 + y2)/2].

In this case, we have the coordinates of one endpoint A(0, 9) and the midpoint M(2, 5).

Let's denote the coordinates of the other endpoint as (x, y).

Using the midpoint formula, we can set up the following equations:

x = (0 + x)/2
y = (9 + y)/2

Simplifying the equations, we get:

2x = 0 + x
2y = 9 + y

Solving each equation, we find:

2x - x = 0
x = 0

2y - y = 9
y = 9

Therefore, the coordinates of the other endpoint are B(0, 9).

To find the coordinates of the other endpoint of line segment AB, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment, given the coordinates of the two endpoints, can be found by taking the average of the x-coordinates and the average of the y-coordinates.

Let's denote the coordinates of the other endpoint as B(x, y).

We are given that the coordinates of A are (0, 9) and the coordinates of M are (2, 5).

Using the midpoint formula, we can set up the following equations:

(x + 0)/2 = 2 (for x-coordinates)
(y + 9)/2 = 5 (for y-coordinates)

Simplifying these equations, we get:

x/2 = 2
y/2 + 9/2 = 5

To solve for x, we can multiply both sides of the first equation by 2:

x = 4

To solve for y, we can subtract 9/2 from both sides of the second equation and multiply both sides by 2:

y/2 = 5 - 9/2
y/2 = 1/2

y = 1

Therefore, the coordinates of the other endpoint B are (4, 1).