# Find the Coordinates of a Point A, Where Ab is a Diameter of a Circle with Center C (2,-3) and the Other End of the Diameter is B (1,4). - Mathematics

Find the coordinates of a point A, where AB is a diameter of a circle with center  C (2,-3)  and the other end of the diameter is B (1,4).

#### Solution

C ( 2,-3) is the center of the given circle. Let  A( a, b) and B (1,4)  be the two end-points of the given diameter AB. Then, the coordinates of C are .

 x = (a+1) /2 , y =( b+4)/2

It is given that  x = 2 and  y=-3.

 ⇒ 2= (a+1)/2 , 3 = (b+4)/2

⇒ 4= a+1 ,-6 = b +4

⇒ a =4-1,b=-6-4

⇒ a=3 , b= -10

Therefore, the coordinates of point A are (3, -10)

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 12