Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint

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 (0,-1) end point (1,-4)

Answer 1

Hi Eden D

(-1, 2))

You just to make use of the Midpoint Formula to solve for the missing coordinate

Midpoint Formula

((x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint (0,-1) end point (1,-4)

Let x₁ = 1, the x coordinate of the endpoint

Let x₂ = the x coordinate of the unknown endpoint

Let y₁ = -4, the y coordinated of the endpoint

Let y₂ = the y coordinated of the unknown endpoint

Just plug in the values and do the calculations

For the x coordinate of the unknown endpoint

(x₁ + x₂)/2

(1 + x₂)/2 = 0

1 + x₂ = 0

x₂ = -1

For the y coordinate of the unknown endpoint

(y₁ + y₂)/2

(-4 + y₂)/2 = -1

-4 + y₂ = -2

y₂ = -2 + 4

y₂ = 2

So the coordinates of the other endpoint are (-1, 2)

Check the arithmetic above if you have any questions send me a message. You can draw or graph your line on a coordinate grid to confirm the position of the other endpoint.

Answer 2

endpoint (1,-4). midpoint (0,-4)

using the midpoint formula

1 + x/2 = 0 solving for x₂

_{x = -1}

also -4 + y/2 = -1

y = 2

so the other endpoint is (-1,2)