how would you solve this math problem: Given AC with endpoint a (16,-6) and midpoint M (3, 7). What are the coordinates of end point C?

Since AM=MC, you can find the coordinates of C by adding to M the difference between A and M

i.e.
Xc = Xm+ (Xm-Xa)
Same goes for Yc.
Watch out for the signs.

(-10.5,5)

(-10.5,7)
(-2.5,7)

To solve this math problem, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are obtained by averaging the coordinates of its endpoints.

The midpoint formula is given as follows:

(x₁+x₂)/2, (y₁+y₂)/2

Here, (x₁, y₁) represents the coordinates of one endpoint, and (x₂, y₂) represents the coordinates of the other endpoint.

In this case, we are given the coordinates of endpoint A as (16, -6) and the coordinates of the midpoint M as (3, 7).

Let's plug these values into the midpoint formula:

(x₁+16)/2 = 3 and (y₁-6)/2 = 7

Solving the first equation, we get:

x₁ + 16 = 2 * 3
x₁ + 16 = 6
x₁ = 6 - 16
x₁ = -10

Solving the second equation, we get:

y₁ - 6 = 2 * 7
y₁ - 6 = 14
y₁ = 14 + 6
y₁ = 20

Therefore, the coordinates of endpoint C are (-10, 20).