Find the coordinates of a point A, where AB i | vedclass

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Question

(A) Let the coordinates of point $A$ be $(x, y).$
Since $AB$ is the diameter of the circle,the center of the circle is the midpoint of the diameter $

Vedclass · Accepted Answer

$(3, -10)$

Vedclass · Answer

(A) Let the coordinates of point $A$ be $(x, y).$
Since $AB$ is the diameter of the circle,the center of the circle is the midpoint of the diameter $AB.$
Given that the center is $(2, -3)$ and point $B$ is $(1, 4).$
Using the midpoint formula,the coordinates of the center are $\left(\frac{x+1}{2}, \frac{y+4}{2}\right).$
Equating this to the given center $(2, -3),$
$\frac{x+1}{2} = 2 \Rightarrow x+1 = 4 \Rightarrow x = 3.$
$\frac{y+4}{2} = -3 \Rightarrow y+4 = -6 \Rightarrow y = -10.$
Therefore,the coordinates of point $A$ are $(3, -10).$

Find the coordinates of a point $A,$ where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4).$

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