Question

3. The centre of a circle is at (-6, 4). If one end of a diameter of the circle is at the origin,
then find the other end.

Answer 1

Let A and B are the end points of diameter and O is the centre of circle.
We know, centre takes place midpoint of diameter.

Here , A(0,0) --------------O(-6,4) -------------B(x,y)
Use section formula of midpoint.
e.g., - 6 = (0 + x)/2
-12 = x
And 4 = (0 + y)/2
8 = y
[ if (x,y) is the midpoint of (x₁y₁) and (x₂,y₂) then, x = (x₁ + x₂)/2 and y= (y₁ + y₂)/2 ]

Hence, other end of diameter = (-12, 8)

Answer 2

GIVEN : One end of the diameter is at origin that is A (0,0).

Let B (a, b) is the another endpoint of the diameter & C(-6,4) is the Centre of the circle. Centre is the mid point of the circle.

Here , we use the midpoint formula
Midpoint = (x₁ + x₂)/2 , (y₁+y₂)/2
Here, x = -6 , y = 4 , x1= 0, y1= 0, x2= a, y2= b

(-6 , 4) = (0 + a)/2 , (0 + b)/2
(-6 , 4) = a/2 , b/2

a/2 = - 6
a = -6 x 2
a = -12

b/2 = 4
b = 4 x 2
b = 8

Hence, the other end point of the diameter is (-12 ,8).

HOPE THIS WILL HELP YOU….