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  • Find the coordinates of a point A, where AB is a diameter of the circle with centre and the point B is <img alt="(2, 6)" src="https://entrancecorner.codecogs.com/

Find the coordinates of a point A, where AB is a diameter of the circle with centre (3, -1) and the point B is (2, 6).

 

 
 
 
 
 

Answers (1)

Given coordinates of O = (3,-1)

          Coordinates of  B = (2,6)

Lets coordinates of  A = (x,y)

\rightarrow We know that the centre of the circles the diameter in equal parts.

\Rightarrow \frac{AO}{BO}=\frac{1}{1}

Apply section formula

(3,-1)=\left ( \frac{x\times 1+2\times 1}{1+1},\frac{y\times 1+6\times 1}{1+1} \right )

\Rightarrow (3,-1)=\left ( \frac{x+2}{2},\frac{y+6}{2} \right )

Now compare both the coordinates,

3,=\frac{x+2}{2} ; -1 = \frac{y+6}{2}

x+2=6\Rightarrow x=4         y+6=-2\Rightarrow y=-8

The coordinates of A=(4,-8)

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Safeer PP

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