Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (w.y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y)
midpoint (2.2), endpoint (1. - 2)
The other endpoint is

Answer 1

Answer:

(3,6)

Step-by-step explanation:

Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:

M(X,Y) = $(\dfrac{x_1+w}{2}, \dfrac{y_1+y}{2})$

From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2

Substituting the given end points into the given formula to get the other end points, we will have;

$X = \dfrac{x_1+w}{2} \\2 = \dfrac{1+w}{2} \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3$

Similarly;

$Y = \dfrac{y_1+y}{2} \\2 = \dfrac{-2+y}{2} \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6$

Hence the other endpoint (w, y) is (3,6)