how to solve this equation

Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)

midpoint

​(−9​,−2​),

endpoint

​(-3​,2​)

Answer 1

The midpoint equations are x_midpoint = (x₁ + x₂)/2 and y_midpoint = (y₁ + y₂)/2

So, plugging in the given points yields: -9 = (x + -3)/2 and -2 = (y + 2)/2

-9 = (x + -3)/2

-18 = x - 3

x = -15

-2 = (y + 2)/2

-4 = y + 2

y = -6

So the coordinates of the other endpoint are (-15, -6)