Algebra Question?

The endpoint of a line segment is (7, 3) and  its midpoint is (8, 15/2).

Algebraically determine the segment's other endpoint.

Endpoint coordinates (x, y) (9, 12).

The midpoint's x and y values are the means of the endpoint's x and y values:

so if your points are:

(x₁, y₁) and (x₂, y₂)

The midpoint is (x_m, y_m):

x_m = (x₁ + x₂) / 2 and y_m = (y₁ + y₂) / 2

You are given one endpoint (7, 3).  I'll call that point 1.

The second endpoint is unknown, I'll call that x and y:

x_m = (7 + x) / 2 and y_m = (3 + y) / 2

The midpoint is (8, 15/2), so we can set x_m and y_m to that, then solve for the unknowns:

8 = (7 + x) / 2 and 15/2 = (3 + y) / 2

Multiply both sides by 2:

16 = 7 + x and 15 = 3 + y

and subtract:

9 = x and 12 = y

The other endpoint is:

(9, 12)