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.
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,
\[- 2 = \frac{2 + x}{2}\]
\[ \Rightarrow - 4 = 2 + x\]
\[ \Rightarrow x = - 6\]
\[\text { And }\]
\[0 = \frac{- 3 + y}{2}\]
\[ \Rightarrow 0 = - 3 + y\]
\[ \Rightarrow y = 3\]
\[\left( x, y \right) = \left( - 6, 3 \right)\]
Solution:-
Since P is the center of the circle and AB is a diameter, the coordinates of point P must be the midpoint of the segment AB. Therefore, we can use the midpoint formula to find the coordinates of point B.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, the coordinates of point A are (2, -3) and the coordinates of point P are (-2, 0), so the coordinates of point B are:
((-2 + 2) / 2, (0 – 3) / 2) = (0, -1.5)
Therefore, the coordinates of point B are (0, -1.5).
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)