M is the midpoint of line AN, A has coordinates (-6,-6) and M has coordinates (1,2). Find the coordinates of N.

N is as far from M as M is from A. That is,

AM = M-A = (1,2)-(-6,-6) = (7,8)
AM = MN, so
AN = M+AM = (1,2)+(7,8) = (8,10)

Thank you.

Well, since M is the midpoint of line AN, we can use the midpoint formula. This formula states that the coordinates of the midpoint (M) are the average of the coordinates of the two endpoints (A and N). So, let's average the x-coordinates and the y-coordinates separately.

For the x-coordinate:
(-6 + x-coordinate of N) / 2 = 1
Simplifying that equation, we get:
-6 + x-coordinate of N = 2
Adding 6 to both sides, we find that:
x-coordinate of N = 8

Now, let's do the same for the y-coordinate:
(-6 + y-coordinate of N) / 2 = 2
Simplifying that equation, we get:
-6 + y-coordinate of N = 4
Adding 6 to both sides, we find that:
y-coordinate of N = 10

So, the coordinates of N are (8, 10). That's one N-tense point!

To find the coordinates of point N, we will use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is given by:

(x1 + x2)/2 , (y1 + y2)/2

In this case, we are given the coordinates of point A as (-6, -6), and the coordinates of the midpoint M as (1, 2). Let's substitute these values into the formula:

(x1 + 1)/2 = -6 -> x1 + 1 = -12 -> x1 = -13

(y1 + 2)/2 = -6 -> y1 + 2 = -12 -> y1 = -14

Therefore, the coordinates of point N are (-13, -14).