how do i solve this? can someone show me a solution so that i can understand the process

Question

One endpoint of the diameter of a circle is at (2, 16) and the center is the midpoint of the diameter of a circle at (-8,4). Find the coordinates of the other endpoint of the diameter.

Answer 1

The process here is visualizing a line that cuts a circle in half by going through its center.

The line starts at the edge of the circle at (2,16) and hits the center at (-8,4)

We're asked to determine the point at which this line ends when it touches the edge of

the circle opposite to where it started.

If you graph the two given points and draw a line connecting them, you can think of this

line as the hypotenuse of a right triangle formed by dropping a vertical from (2,16) and

extending a horizontal to the right from (-8,4). The legs of this triangle are a vertical 12

and a horizontal 10.

Now if you drop a vertical 12 from (-8,4) and extend from where it ends a horizontal 10

to the left, you'll get to the end point of the circle's diameter, because the distance from

this end point to (-8,4) is the same as the distance from (-8,4) to (2,16).

Answer 2

one endpoint is (2,16), the circle's center is (-8,4). The other endpoint is on a line that runs through the center point. The distance from one endpoint to the center equals the distance from the center to the other end point

2 to -8 = 10, 16 to 4 = 12

subtract 10 from -8 to get -18 for the x coordinate of the other end point

subtract 12 from 4 to get -8 for the y coordinate of the other endpoint

the other end point is (-18,-8)

It may help to graph the circle, center and end points

the equation for the circle is: (x+8)^2 + (y-4)^2 = 244 = r^2

construct 2 right triangles, with base 10 and height 12

and hypotenuse = square root of 100+144 = 244

radius of the circle is sqr244=about 15.6