How do you find the coordinates of the other endpoint of a segment with the given A are (-2,3) and the coordinates of midpoint M are (1,0)?

To find the coordinates of the other endpoint of the segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) of a segment with endpoints (x₁, y₁) and (x₂, y₂) can be found by taking the average of the x-coordinates and the average of the y-coordinates.

In this case, we are given the coordinates of endpoint A as (-2, 3) and the coordinates of midpoint M as (1, 0). Let's denote the coordinates of the other endpoint as (x, y).

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

(x + (-2))/2 = 1 (for the x-coordinates) (y + 3)/2 = 0 (for the y-coordinates)

Simplifying these equations, we get:

(x - 2) = 2 (y + 3) = 0

Solving for x and y, we find:

x = 4 y = -3

Therefore, the coordinates of the other endpoint of the segment are (4, -3).

The midpoint is found from averaging the x-values of the endpoints and averaging the y-values.