A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

This is the formula of finding the center of two point

x=1/2(x1+x2)
y=1/2(y1+y2)

but what if the center is given and you have to find the other end,.,what is the formula?

Originally Posted by jasonlewiz

A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

This is the formula of finding the center of two point

x=1/2(x1+x2)
y=1/2(y1+y2)

but what if the center is given and you have to find the other end,.,what is the formula?

1. Let $\displaystyle C(x_C, y_C)$ the midpoint of a line segment (in your case it is a diameter). Then your formula becomes:

$\displaystyle \begin{array}{l}x_C=\frac12(x_1+x_2) \\y_C=\frac12(y_1+y_2)\end{array}$

2. You must know the coordinates of 2 points to calculate the coordinates of the third one. For instance: If you know the coordinates of the midpoint and the coordinates of $\displaystyle P(x_1, y_1)$ then you have to solve the equations for $\displaystyle x_2$ respectively for $\displaystyle y_2$

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Originally Posted by jasonlewiz

A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

This is the formula of finding the center of two point

x=1/2(x1+x2)
y=1/2(y1+y2)

but what if the center is given and you have to find the other end,.,what is the formula?

for x coordinate of the other end:
$\displaystyle 5 = \frac{x + 6}{2}$
for y-coordinate of the other end:
$\displaystyle 1 = \frac{y + 3}{2}$

Hello, jasonlewiz!

A circle with the center at C(5,1) has a diameter that terminates at A(6,3).
Find the other end of the diameter.

Did you make a sketch? . . . The answer will be obvious.

Code:

      |               A
      |               o
      |               ↑
      |               ↑2
      |         C     ↑
      |   + ← ← o → → +
      |   ↓        1
    --+---↓-----+----------
      |   ↓     5
      |   o
      |   B

To get from the center $\displaystyle C(5,1)$ to point $\displaystyle A(6,3)$,
. . we move 1 unit right and 2 units up.

Hence, to get the other end of the diameter $\displaystyle B$,
. . we start at $\displaystyle C$ and move 1 unit left and 2 units down.

Got it?