Question

If AB is a diameter and 0(2, -3) is center of a circle. If coordinates of B are (1, 4), then find the coordinates of A​

Answer 1

Given :

• A Circle with Centre O (2,-3)
• AB is a Diameter of the Circle with B (1,4)

Find :

• Co-ordinates of A

Solution :

∴ AB is the Diameter, the centre will be the mid Point of AB

$\sf \: Let \: A \: be \: (x, y)$

Applying Mid Point Theorem

Centre of the Circle is the mid point of AB

$\sf \: X - Coordinators \: of \: AB = \frac{x + 1}{2} \\ \ \ \: \sf\sf Y - Coordinators \: of \: AB = \frac{y + 4}{2}$

But, Given Centre Co-ordinates

(2, -3)

$\boxed{ \sf \: \frac{x + 1}{2} = 2} - - (1)\\ \\ \boxed{\sf \frac{y + 4}{2} = - 3 } - - (2)$

Find the Value of X with the help of equation 1st

$\rightarrow \sf \: \frac{x + 1}{2} = 2 \\ \rightarrow\sf x + 1 = 4 \\ \rightarrow \sf \: x = 4 - 1 \\ : \implies \sf \red{ \boxed{ \sf \green{x = 3}}}$

Find the value of Y with the help of Equation 2nd

$\rightarrow \sf \: \frac{y + 4}{2} = - 3 \\ \rightarrow \sf \: y + 4 = - 6 \\ \rightarrow \sf y = - 6 - 4 \\ \sf : \implies \red{\boxed { \sf \green{y = - 10}}}\:$

• The Co-ordinates of A is ( 3, - 10 )

☆ For Diagram refer to the Attachment!!

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