Question

OS

Question 2
A circle has a centre C (1,3)The end points of a diameter of the circle are A (-3,2k) and B (5,k)
Find the value of k, k

Answer 1

k = 2

Explanation:

We'll need the Midpoint Formula: the midpoint of a segment joining points
`(x_1, y_1) \text{ and }(x_2, y_2) \text{ is } \left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`. In other words, average the x's, then average the y's.

The midpoint of a diameter is the centre of the circle!

The midpoint of the segment joining (-3, 2k) and (5, k) is

`\left((-3+5)/(2), (2k+k)/(2) \right)=\left(1,(2k+k)/(2)\right)=\left(1,(3k)/(2)\right)`

That last expression is the centre of the circle; it is the same as (1, 3).

`\left(1,(3k)/(2)\right)=\left(1,3\right)\\(3k)/(2)=3\\3k=6\\k=2`