SOLUTION: The ednpoint of a diameter of a circle is (-1,6). If the center is at (2,-1), find the other endpoint of the diameter passing through (-1,6)

Question 883631: The ednpoint of a diameter of a circle is (-1,6). If the center is at (2,-1), find the other endpoint of the diameter passing through (-1,6)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Find the radius using Distance Formula for points (-1,6) and the center(2,-1)....

There is an alternative. The center and the given endpoint form a line. The other endpoint is a point on this line. Now, using Distance formula, and knowing the equation of this line, you are looking for the point this way:

D, (-1,6) to (2,-1) SAME AS D, (x,y) to (2,-1).

---actually this is just the equation of the circle.

The line containing given endpoint and circle center:

y=mx+b
b=y-mx

-
.

WHAT NEXT TO DO?
Substitute for y in the circle equation, simplify, and solve for x. You will get two values. The one you are looking for is the solution OTHER THAN x=-1. Now, use it to find y.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The ednpoint of a diameter of a circle is (-1,6). If the center is at (2,-1), find the other endpoint of the diameter passing through (-1,6)

Use the midpoint formula: (,), equating each coordinate to the midpoint coordinates to determine
the other endpoint. Remember that you're trying to find and .
Then do a check!!
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