Question

Find the coordinates of a point A, where AB is the diameter of a circle whose center is (4,-1) and B is (5,2).

Answer 1

The coordinates of the point A is (3,-4).

• Let the center of the circle be C (4,-1).
• As AB is the diameter of the circle,

Therefore the center of the circle C will be the midpoint of the diameter AB.

• Let us assume the point A(x,y).
• Since C is the midpoint of segment AB.

x-coordinate of C = $\frac{x_1+x_2}{2}$

y-coordinate of C = $\frac{y_1+y_2}{2}$

where ,

x₁=x and y₁=y

x₂=5 and y₂=2

• x-coordinate of C = $\frac{x+5}{2}$

4 = $\frac{x+5}{2}$

8 = x + 5

x = 3

• y-coordinate of C = $\frac{y+2}{2}$

-1 = $\frac{y+2}{2}$

-2 = y + 2

y = -4

• Hence the coordinates of A(3,-4)