Find the coordinates of the point $A$, where $AB$ is the diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4)$.
Step-by-Step Solution
Key Concept: Centre $C(2, -3)$ is midpoint of $A(x, y)$ and $B(1, 4)$.<br>$\dfrac{x + 1}{2} = 2 \Rightarrow x = 3$, $\dfrac{y + 4}{2} = -3 \Rightarrow y = -10$. $A(3, -10)$.
$\dfrac{x + 1}{2} = 2 \Rightarrow x + 1 = 4 \Rightarrow x = 3$. [1.0 Mark]
$\dfrac{y + 4}{2} = -3 \Rightarrow y + 4 = -6 \Rightarrow y = -10$. Point $A$ is $(3, -10)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $x = 3$: 1.0 Mark
Solving $y = -10 \Rightarrow A(3, -10)$: 1.0 Mark
Correct Answer: