Question

Joelle was asked to find the missing endpoint of a segment when given an endpoint of –6 +3i and a midpoint of –13 + i. Her work is shown below.

Her mistake was...


A. not subtracting the a and b in the original equations.

B. writing the final answer as 1+ 5i instead of 5 + i.

C. switching the endpoint and midpoint in her original equations.

D. not using –6 and 3 in one of her original equations and –13 and 1 in the other original equation.

Answer 1

C

Explanation:

`(-6+a)/(2) =-13\\-6+a=-13*2\\a=-26+6\\a=20\\(3i+b i)/(2)=i\\\\ \\3+b=2\\b=2-3=-1\\`

middle point is 20-i

Answer 2

C. switching the endpoint and midpoint in her original equations.

Explanation:

One endpoint is –6 +3i

The other endpoint is a + bi (where a and b are unknown)

The midpoint is -13 + i. Its coordinates are obtained as follows:

coordinate of the midpoint = (coordinate of one endpoint + coordinate of the other endpoint)/2

For this case:

-13 = (-6 + a)/2

1 = (3 +b)/2