Question

in the adjoining figure PQ is a diameter of a circle with centre of the coordinates of the point p and q are respectively 3, - 10 and 1, 4 then the coordinates of o r​

Answer 1

hope this answer will be helpful

Answer 2

Centre O (2, -3)

Radius = 14.14 units

Step-by-step explanation:

Given: PQ is a diameter of a circle.

P (3, - 10) and Q (1, 4)

Find: Coordinates of centre O and radius r.

Solution:

Midpoint of a line segment AB is the point that is equidistant from the endpoints A and B. d(A, B) = √ (x1 - x2)² + (y1 - y2)². It does not matter in what order you subtract the x−coordinates or the y−coordinates.

x1 = 3; y1 = -10

x2 = 1; y2 = 4

Mid-point of PQ = √ (3 - 1)² + (-10 - 4)²

= √ (2)² + (-14)²

= √4 + 196

= √200

Radius r = 14.14 units

Co-ordinates of the centre O = (x1 - x2) / 2 ; (y1 - y2) / 2  

=  (3+1) / 2;  (-10+4) / 2

= (2, -3)