Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.

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Solution

Centre = P(–2, 0)
Diameter has A(2, –3) on one end and B(x, y) on the other.
The centre point P divides AB in two equal parts.
So, using the midpoint formula,
$- 2 = \frac{2 + x}{2} \Rightarrow - 4 = 2 + x \Rightarrow x = - 6 And 0 = \frac{- 3 + y}{2} \Rightarrow 0 = - 3 + y \Rightarrow y = 3 (x, y) = (- 6, 3)$

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Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.

Centre = P(–2, 0) Diameter has A(2, –3) on one end and B(x, y) on the other. The centre point P divides AB in two equal parts. So, using the midpoint formula, -2=2+x2⇒-4=2+x⇒x=-6And0=-3+y2⇒0=-3+y⇒y=3x,y=-6,3