Question

A segment has an endpoint at (1,−2). The midpoint is at (−4,−2). What are the coordinates of the other endpoint?

Answer 1

Given endpoints are (x₁,y₁) = (1,-2) and Midpoints (-4,-2)

Let the coordinates of the other endpoint be (x₂,y₂).

We know that Coordinates of the midpoint of a line is given by:

⇒ (x₁ + x₂/2, y₁ + y₂/2)

⇒ (1 + x₂/2, -2 + y₂/2) = (-4,-2)

(i)

⇒ (1 + x₂)/2 = -4

⇒ 1 + x₂ = -8

x₂ = -9.

(ii)

⇒ (-2 + y₂)/2 = -2

⇒ y₂ = -4 + 2

⇒ y₂ = -2

Therefore, the coordinates of the other endpoint is (-9,-2).

Hope it helps!