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

(3,6)

Explanation:

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

M(X,Y) =
`((x_1+w)/(2), (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 = (x_1+w)/(2) \\2 = (1+w)/(2) \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3`

Similarly;

`Y = (y_1+y)/(2) \\2 = (-2+y)/(2) \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6`

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