Question

A circle has its center at (10,4). One endpoint of the diameter is at (2,-6), find the other endpoint of that diameter.

Answer 1

Answer: The second end point of the diameter is (18, 14)

The centre of the circle is (10, 4)

one end point of the diameter is at (2, -6)

Since, the center of the circle is the mid point of the circle

The mid point = (10, 4)

`\begin{gathered} \text{mid point = (}\frac{x1\text{ + x2}}{2},\text{ }\frac{y1\text{ + y2}}{2}) \\ \text{for x } \\ Let\text{ the first point = A} \\ \text{Let the second point = B} \\ A\text{ = (2, -6)} \\ To\text{ calculate poin B} \\ x1=\text{ 2, and y1 = -6} \\ \text{Let the mid point be = (xc , yc)} \\ xc\text{ = }\frac{x1\text{ + x2}}{2} \\ xc\text{ = 10, x1 = 2} \\ 10\text{ = }\frac{2\text{ + x2}}{2} \\ \text{Cross multiply} \\ 10\text{ x 2 = 2 + x2} \\ 20\text{ = 2 + x2} \\ x2\text{ = 20 - 2} \\ x2\text{ = 18} \\ To\text{ calculate y2} \\ yc\text{ = }\frac{y1\text{ + y2}}{2} \\ yc\text{ = 4, and y1 = -6} \\ 4\text{ = }\frac{-6\text{ + y2}}{2} \\ \text{4 x 2 = -6 + y2} \\ 8\text{ = -6 + y2} \\ y2\text{ = 8 + 6} \\ y2\text{ = 14} \\ \text{Therefore, the second end point = (18, 14)} \end{gathered}`