Answer:
The other end point is -7 + i
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