The coordinates of point B are (-4 , -2) ⇒ answer H
Step-by-step explanation:
In any circle
- The diameter of the circle passing through its center
- The center of the circle is the mid-point of all diameters
If (x , y) are the coordinates of the mid-point of a line whose end
points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] , then
[tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ Point C is the center of a circle
∵ AB is the diameter of the circle
∴ C is the mid point of AB
∵ A = (2 , 6) ⇒ [tex](x_{1},y_{1})[/tex]
∵ B = [tex](x_{2},y_{2})[/tex]
∵ C = (-1 , 2) ⇒ (x , y)
- Use the rule of the mid-point above
∵ [tex]-1=\frac{2+x_{2}}{2}[/tex]
- Multiply both sides by 2
∴ -2 = 2 + [tex]x_{2}[/tex]
- Subtract 2 from both sides
∴ [tex]x_{2}[/tex] = -4
∴ The x-coordinate of point B is -4
∵ [tex]2=\frac{6+y_{2}}{2}[/tex]
- Multiply both sides by 2
∴ 4 = 6 + [tex]y_{2}[/tex]
- Subtract 6 from both sides
∴ [tex]y_{2}[/tex] = -2
∴ The y-coordinate of point B is -2
The coordinates of point B are (-4 , -2)
Learn more:
You can learn more about the circle in brainly.com/question/9510228
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