Circle C has diameter AB. The coordinates of A are (5,1) and the coordinates of C are (6,10). Find the coordinates of B.

(7, 19)

Step-by-step explanation:

We know that we are talking about circle C, which means that the center is point C. Since the diameter is AB, that means that AB goes through the center C and that center C is the midpoint of the segment AB.

Say the coordinates of B are (x, y). We can use the Midpoint Theorem to figure out B. The Midpoint Theorem states that for two points and , the coordinates of the midpoint are: .

Here, our two points are A(5, 1) and B(x, y). Then, the midpoint is: . We already know the midpoint is C(6, 10), so we can just set 6 equal to and set 10 equal to :

6 =  ⇒  12 = 5 + x  ⇒  x = 12 - 5 = 7

AND

10 =  ⇒  20 = 1 + y  ⇒  y = 20 - 1 = 19

So, the coordinates of B is: (7, 19).

Hope this helps!

(7 , 19)

Step-by-step explanation:

Centre is the midpoint of the diameter

C = Midpoint of AB

Let B: (x,y)

(6,10) = (x+5)/2, (y+1)/2

12 = x + 5

x = 7

20 = y + 1

y = 19

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.

no

step-by-step explanation: