Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ Midpoint: (-26,-1) Endpoint: (-19,-4)

Question

(Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)

Answer 1

You can do this problem in different ways. You can use the midpoint formula which is Midpoint = (x₁+x₂/2, y₁+y₂/2), in which case you would take your midpoint and set it equal to the formula, like so:

(-26, -1) = (-19+x₂/2, -4+y₂/2)

You will then set up two equations from corresponding values. In other words:

-26 = -19+x₂/2 and -1 = -4+y₂/2

In which case you would solve for x₂ and y₂ (multiply both sides by 2 and add/subtract the constant), and put them into the ordered pair (x₂, y₂).

You can also use slope, which is (y₂-y₁)/(x₂-x₁). Calculate the slope from endpoint to midpoint, then apply the slope once more from the midpoint to the other endpoint.

Answer 2

You can still use the midpoint formula xm=(x1+x2)/2 to solve this problem, but instead of plugging in for x1 and x2 you are plugging in for x1 and xm to get the equation -26=(-19+x2)/2. Solving this equation will get you the x coordinate of the other endpoint. You need to repeat the same steps to get the y-coordinate.