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The line segment joining A(-3, 1) and B(5, -4) is a diameter of a circle whose centre is C. Find the coordinates of the point C.

Section Formula

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Answer

Given, C is the centre of the circle and AB is the diameter.

C is the midpoint of AB.

Let coordinates of C be (x, y)

∴x=x1+x22,y=y1+y22⇒x=−3+52,y=1+(−4)2⇒x=22,y=−32⇒x=1,y=−32.\therefore x = \dfrac{x1 + x2}{2}, y = \dfrac{y1 + y2}{2} \\[1em] \Rightarrow x = \dfrac{-3 + 5}{2}, y = \dfrac{1 + (-4)}{2} \\[1em] \Rightarrow x = \dfrac{2}{2}, y = -\dfrac{3}{2} \\[1em] \Rightarrow x = 1, y = -\dfrac{3}{2}.

Hence, coordinates of C are (1,−32)(1, -\dfrac{3}{2}).

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