I'm having a hard time with this question:

"AB has endpoints A(n,4n) and B(3n,6n).
Which of the following is true?
A. AB=4n
B. The midpoint of AB is (2n,2n).
C. AB=n√8
D. The midpoint of AB is (4n,10n)".
PLEASE HELP!!!!!

AB = √(3n-n)^2+(6n-4n)^2 = √(4n^2+4n^2) = n√(8)

midpoint = (2n,5n)

looks like only C

Thanks!!!!

To solve this problem, we need to use the distance formula and midpoint formula. Let's break it down step by step.

1. Distance formula:
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)

2. Midpoint formula:
The midpoint formula is given by:
M = ((x1 + x2)/2, (y1 + y2)/2)

Now let's apply these formulas to the given problem.

Endpoint A is at A(n, 4n), and endpoint B is at B(3n, 6n).

1. To find the length of AB, use the distance formula:
AB = √((3n - n)^2 + (6n - 4n)^2)
= √((2n)^2 + (2n)^2)
= √(4n^2 + 4n^2)
= √(8n^2)
= 2n√2 (since √8 = √(4 * 2) = 2√2)

So, option C "AB = n√8" is true.

2. To find the midpoint of AB, use the midpoint formula:
M = ((n + 3n)/2, (4n + 6n)/2)
= (4n/2, 10n/2)
= (2n, 5n)

So, option D "the midpoint of AB is (4n, 10n)" is false.

Therefore, the answer is option C, "AB = n√8" is true.

I hope this clears up the confusion and helps you solve the problem! Let me know if you have any further questions.