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 ​(​1,6​), endpoint ​(-2​,​1)

Answer 1

(4,11)

Explanation:

Given two coordinates (x₁, y₁) and (x₂,y₂), the midpoint of the coordinates is expressed as M(X,Y) =
`((x_1+x_2)/(2), (y_1+y_2)/(2))` where;

`X = (x_1+x_2)/(2)\ and \ Y = (y_1+y_2)/(2)`

Given the midpoint (X, Y) = (1,6) and one end point to be ​(-2​,​1), to get the unknown endpoint (x,y), we will apply the formula above. from the coordinates given X = 1, Y = 6, x₁ = -2 and y₁ = 1

`Given \ X = (x_1+x_2)/(2)\\1 = (-2+x)/(2)\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4`

Similarly to get y;

`Given \ Y = (y_1+y)/(2)\\6 = (1+y)/(2)\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11`

Hence the unknown endpoint (x,y) is (4,11)