Question

The coordinates of one end point of a diameter of a circle (4,-1) and the coordinates of the center are (1,-3). Find the coordinates of the other end of the diameter.

Answer 1

Let AB be the diameter of the circle center "C"

Let A (4, -1), B (x, y) and C (1, -3)

"C" is the midpoint of AB

⟹4+x2=1⟹x=−2

⟹1−y2=−3⟹y=−5

HenceB=(−2,−5)

Answer 2

Answer: The answer is (-2,-5).

Step-by-step explanation:  As shown in the attached figure, C is a circle with centre O(1,-3). AB is a diameter of the circle where co-ordinates of one end are A(4,-1). We need to find the co-ordinates of point B, which the other end of the diameter AB.  

Let the co-ordinates of point B be (a,b). Since the centre lies in the middle of the diameter, so the point O will divide the diameter AB in the ratio 1:1.

So, we can write

$(1,-3)=(\dfrac{4+a}{2}, \dfrac{-1+b}{2})\\\\\Rightarrow \dfrac{4+a}{2}=1\\\\\Rightarrow 4+a=2\\\\\Rightarrow a=-2.$

and

$\dfrac{-1+b}{2}=-3\\\\\Rightarrow -1+b=-6\\\\\Rightarrow b=-5.$

Thus, the co-ordinates of the other end B are (-2,-5).