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

Answer:

(4,11)

Step-by-step explanation:

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

$X = \dfrac{x_1+x_2}{2}\ and \ Y = \dfrac{y_1+y_2}{2}$

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

$Given \ X = \dfrac{x_1+x_2}{2}\\1 = \dfrac{-2+x}{2}\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4$

Similarly to get y;

$Given \ Y = \dfrac{y_1+y}{2}\\6 = \dfrac{1+y}{2}\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11$

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