Question

if A and B ( 5,3 ) are two ends points of a diameter of the circle and its centre is ( 3,2 ) then find A

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The coordinates of A are ( 1, 1 ).

Step-by-step-explanation:

We have given the coordinates of one end of a diameter and the centre of the circle.

We have to find the coordinates of the other end of the diameter.

Let the point O be the centre of the circle.

$\sf\:A\:\equiv\:(\:x_{1}\:,\:y_{1}\:)\\\\\sf\:B\:\equiv\:(\:5\:,\:3\:)\:\equiv\:(\:x_{2}\:,\:y_{2}\:)\\\\\sf\:O\:\equiv\:(\:3\:,\:2\:)\:\equiv\:(\:x\:,\:y\:)\\\\\sf\:Now,\:by\:using\:midpoint\:formula,\\\\\pink{\sf\:x\:=\:\dfrac{x_{1}\:+\:x_{2}}{2}\:\:,\:\:y\:=\:\dfrac{y_{1}\:+\:y_{2}}{2}}\:\:\:\sf\:-\:-\:[\:Centre\:is\:the\:midpoint\:of\:the\:diameter\:]\\\\\implies\sf\:3\:=\:\dfrac{x_{1}\:+\:5}{2}\:\:,\:\:2\:=\:\dfrac{y_{1}\:+\:3}{2}\\\\\implies\sf\:6\:=\:x_{1}\:+\:5\:\:,\:\:4\:=\:y_{1}\:+\:3\\\\\implies\sf\:x_{1}\:=\:6\:-\:5\:\:,\:\:y_{1}\:=\:4\:-\:3\\\\\implies\boxed{\red{\sf\:x_{1}\:=\:1\:\:,\:\:y_{1}\:=\:1}}$

The coordinates of A are ( 1, 1 ).

Additional Information:

1. Section Formula:

The formula which is used to find the coordinates of a point which divides a line segment in a particular ratio is called section formula.

$\large{\boxed{\red{\sf\:x\:=\:\dfrac{mx_{2}\:+\:nx_{1}\:}{m\:+\:n}}}}\:\:\sf\:\&\:\:\:\large{\boxed{\red{\sf\:y\:=\:\dfrac{my_{2}\:+\:ny_{1}\:}{m\:+\:n}}}}$

2. Midpoint Formula:

The formula which is used to find the coordinates of the midpoint of a segment is called the midpoint formula.

When a point is midpoint of a segment, then the ratio in which it divides the segment is always 1 : 1.

$\large{\boxed{\red{\sf\:x\:=\:\dfrac{x_{1}\:+\:x_{2}}{2}\:\:,\:\:y\:=\:\dfrac{y_{1}\:+\:y_{2}}{2}\:\:}}}$