Question

Let (-3, 2)be one end of a diameter of a circle with centre (4, 6) Find the other end of the diameter

• A. (11, 10)
• B. (10, 2)
• C. (1,1)
• D. (7, 5)

Answer 1

The correct option is A (11, 10)

Centre of the circle is at the midpoint of the diameter.
Let the other end of the diameter be $(x,y)$
Midpoint of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
So midpoint of the diameter $(\frac{-3+x}{2},\frac{2+y}{2})=(4,6)$
Equating both the co-ordinates, we get
$\frac{-3+x}{2}=4=>x=11$
And $\frac{2+y}{2}=6=>y=10$
So, the other end of the diameter is is $(11,10)$