Question

AB is diameter of the circle whose centre is (2, – 3)
and B is the point (3, 4). The coordinates of a point
A will be

Answer 1

Coordinate of point A is ( 1 , - 10) where AB is Diamter of circle whose center is (2 , -3) and B is point ( 3 , 4)

Given :

• A Circle with center (2 , - 3)
• Diameter AB
• B = (3 , 4)

To Find :

• Coordinates of point A

Concept to be used :

 Center is mid point of diameter

 Formula for mid point of (x₁ , y₁) and (x₂ , y₂ ) :

$\left(\dfrac{x_1+x_2}{2} ,\dfrac{y_1+y_2}{2}\right)$

Step 1 :

Assume that coordinate of point A is ( x , y)

Step 2 :

Find mid point of A (x , y) and B (3 , 4) using mid point formula

$\left(\dfrac{x +3}{2} ,\dfrac{y +4 }{2}\right)$

Step 3 :

Equate the coordinate with center of circle ( 2 , - 3)

$\dfrac{x +3}{2} = 2 ,\quad \dfrac{y +4 }{2}=-3$

Step 4 :

Solve for x and y

x + 3 = 4    ,  y + 4  = -6

x = 1           ,  y = - 10

Coordinate of point A is ( 1 , - 10) where AB is Diamter of circle whose center is (2 , -3) and B is point ( 3 , 4)