Question

The centre of a circle is (2, –3) and one end of a diameter is (1, 4), find the other end.

Answer 1

Step-by-step explanation:

here o is the mid point with coordinated (2,-3)

and B(1,4)

by using miss point formula we can find the other end of diameter that is coordinates of point A

final ans we get A(3,-10)

pls look into the image attached for better understanding

hope it helps

Answer 2

Answer:

The coordinate of the other end of the diameter is $(3,-10).$

Step-by-step explanation:

Let the other end of the diameter of the given circle be $B(x_2,y_2)$ whose one end is $A(1,4).$

Mid point of $AB$ is $(\frac{1+x_2}{2} ,\frac{4+y_2}{2} ).$

Since the centre $C(2,-3)$ of the circle is the mid point of $AB,$ $\frac{1+x_2}{2} =2$  and  $\frac{4+y_2}{2} =-3$

⇒ $x_2=3$ and $y_2=-10.$

Therefore the coordinate of the other end of the diameter is $(3,-10).$