M is the midpoint of AN, A has coordinates (-7,4), and M has coordinates (-4, -1). Find
the coordinates of N.
Help explain pls?

Step-by-step explanation:

According to Question , M is the midpoint of AN, A has coordinates (-7,4), and M has coordinates (-4, -1).

Figure :-

Let the coordinates of N be ( x , y )

Now , according to Midpoint Formula , the midpoint of points say A(x , y) and B (x' , y') is given by ,

On using this formula ,

Explanation:

Let's focus on the x coordinates of each point for now.

The idea to find the midpoint's coordinates is to add up the endpoints coordinates and divide by 2.

So we'll add up -7 and x, then divide by 2 to get the midpoint x coordinate of -4

In short we have:  (-7+x)/2 = -4

Solving for x leads to...

(-7+x)/2 = -4

-7+x = 2*(-4)

-7+x = -8

x = -8+7

x = -1

This is the x coordinate of point N

We'll repeat the same idea and steps for the y coordinates

So,

(4+y)/2 = -1

4+y = 2(-1)

4+y = -2

y = -2-4

y = -6

This is the y coordinate of point N.

In summary, we found that point N is located at (-1, -6)

Point A is (-7,4) and point N is (-1,-6)

If you apply the midpoint formula to those two points, you should find the midpoint to be M(-4,-1) which helps confirm the answer.

Another way to confirm the answer is to compute the distance from A to M, which finds the length of segment AM. Do the same for segment MN. You should find that both segments are the same length.

The diagram below is a visual way to check. Starting at point A and moving down to point B, we moved 5 units. Then go from B to M and you'll move 3 units to the right. This pattern "down 5, right 3" is applied again when we go from M to C to N in that order. This effectively creates two congruent triangles (ABM and MCN) which can lead to proving AM = MN.

In short: the red piece of the graph is the same length as the blue piece; this confirms we have the correct answer.