Question : The point P is the midpoint of the segment AB. The coordinates of point P are (2, 1) and that of point A are (11, 5). The coordinates of point B are:
Option 1: (–7, –3)
Option 2: (6.5, 3)
Option 3: (7, 3)
Option 4: (–6.5, –3)
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Correct Answer: (–7, –3)
Solution : Given: The coordinates of the point A are (11, 5). Let the co-ordinates of the point B be $(x,y)$. Since, the point P (2, 1) is the mid-point, ⇒ $2=\frac{11+x}{2}$ ⇒ $2×2=11+x$ ⇒ $x=–7$ Similarly, $1=\frac{5+y}{2}$ ⇒ $1×2=5+y$ ⇒ $y=–3$ So, the coordinates of B are (–7,–3). Hence, the correct answer is (–7,–3).
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