Question

on the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3) what are the center and raduis of the wheel

Answer 1

The center is (8,6) and radius is 5 units of the wheel

Explanation:

On the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3)

End point of diameter is (4 9) and (12,3)

As we know mid point of diameter is center of circle.

Mid point formula:

`(x,y)\rightarrow ((x_1+x_2)/(2),(y_1+y_2)/(2))`

Mid point of (4 9) and (12,3)

`Centre: ((4+12)/(2),(9+3)/(2)`

Center: (8,6)

Radius is distance between center and any one end point of diameter.

Distance formula:

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`

`R=\sqrt{(8-4)^2+(6-9)^2`

`R=√(16+9)=√(25)`

Radius = 5

Hence, The center is (8,6) and radius is 5 units of the wheel

Answer 2

The center of the circle is point (8 , 6)

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)