Asegment in the complex plane has a midpoint at −1.5 + 3.5i. if one endpoint of the segment is at 4 + 6i, what is the other endpoint?

The other end point is -7 + i

Step-by-step explanation:

* Lets revise how to find the mid-point in the complex plane

- The midpoint x + yi of the line segment joining two complex

 numbers a + bi and s + ti is the average of the numbers at the endpoints.

- Midpoint Formula in the Complex Plane:

 The Midpoint ⇒ x + yi = (a + s)/2 + [(b + t)/2]i

∴ x = (a + s)/2 , y = (b + t)/2

* Now lets solve the problem

- The mid-point of a segment in complex plane is -1.5 + 3.5i

- One end point of the segment is 4 + 6i

- Let -1.5 + 3.5i = x + yi and 4 + 6i = a + bi

- We want to find point s + ti

∵ x = (a + s)/2

∴ -1.5 = (4 + s)/2 ⇒ multiply the two sides by 2

∴ -3 = 4 + s ⇒ subtract 4 from both sides

∴ -7 = s ⇒ s = -7

∵ y = (b + t)/2

∴ 3.5 = (6 + t)/2 ⇒ multiply the two sides by 2

∴ 7 = 6 + t ⇒ subtract 6 from both sides

∴ 1 = t ⇒ t = 1

* The other end point is -7 + i

step-by-step explanation: