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Sagot :
The centre of the circle is at (1, -2).
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Note that the centre of the circle is also the midpoint of the diameter of the circle. This is because the centre of the circle separates the diameter into two equal line segments called the radii, which tells us that the centre of the circle is the midpoint of the diameter, by the definition of a midpoint. So, to find the centre of the circle given the endpoints of the diameter, we will solve for the midpoint by using the midpoint formula.
The midpoint formula is expressed below:
[tex]\boxed{\displaystyle M=\bigg(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigg)}[/tex]
Based on the problem, we let:
[tex](x_1,y_1)=(-1,-1) \quad \quad (x_2,y_2)=(3,-3)[/tex]
Substitute the coordinates to the midpoint formula.
[tex]\displaystyle M=\bigg(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigg)[/tex]
[tex]\displaystyle M=\bigg(\frac{-1+3}{2},\frac{-1+(-3)}{2}\bigg)[/tex]
[tex]\displaystyle M=\bigg(\frac{2}{2},\frac{-4}{2}\bigg)[/tex]
[tex]M=(1,-2)[/tex]
Therefore, the midpoint or the centre of the circle is at (1, -2).
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Hope it helps.
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