Answer:
The center of the circle is point (8 , 6)
Step-by-step explanation:
* At first lets revise how to find the mid-point between two points
- If (x1 , y1) and (x2 , y2) are the end point of a segment
- If (x , y) is the mid-point of this segment
- To find x add x1 and x2, then divide the answer by 2
∴ x = (x1 + x2)/2
- Similar to find y add y1 and y2, then divide the answer by 2
∴ y = (y1 + y2)/2
∴ The mid-point (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]
* Now lets solve the problem
- The center of the circle is the mid-point of the diameter
- Consider the center of the circle is (x , y)
- (x , y) is the mid-point of the diameter of the circle with endpoints
(4 , 9) and (12 , 3)
- Let (4 , 9) is (x1 , y1) and (12 , 3) is (x2 , y2)
∵ x1 = 4
∵ x2 = 12
∵ x = (x1 + x2)/2
∴ x = (4 + 12)/2 = 16/2 = 8
* Similar
∵ y1 = 9
∵ y2 = 3
∵ y = (y1 + y2)/2
∴ y = (9 + 3)/2 = 12/2 = 6
∴ (x , y) = (8 , 6)
* The center of the circle is point (8 , 6)
