Question

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.

Answer 1

Answer:

(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 $(x_1,y_1)$ and $(x_2,y_2)$, the coordinates of the midpoint are: $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$.

Here, our two points are A(5, 1) and B(x, y). Then, the midpoint is: $(\frac{5+x}{2} ,\frac{1+y}{2} )$. We already know the midpoint is C(6, 10), so we can just set 6 equal to $\frac{5+x}{2}$ and set 10 equal to $\frac{1+y}{2}$:

6 = $\frac{5+x}{2}$  ⇒  12 = 5 + x  ⇒  x = 12 - 5 = 7

AND

10 = $\frac{1+y}{2}$  ⇒  20 = 1 + y  ⇒  y = 20 - 1 = 19

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

Hope this helps!

Answer 2

Answer:

(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