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Question
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,
\[- 2 = \frac{2 + x}{2}\]
\[ \Rightarrow - 4 = 2 + x\]
\[ \Rightarrow x = - 6\]
\[\text { And }\]
\[0 = \frac{- 3 + y}{2}\]
\[ \Rightarrow 0 = - 3 + y\]
\[ \Rightarrow y = 3\]
\[\left( x, y \right) = \left( - 6, 3 \right)\]
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