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).