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

alanisalvarez2000 alanisalvarez2000    1   14.02.2022 04:30    3

annamariaafowyhrq annamariaafowyhrq  14.02.2022 04:30

k = 2

Step-by-step 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(\frac{x_1+x_2}{2},\frac{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(\frac{-3+5}{2}, \frac{2k+k}{2} \right)=\left(1,\frac{2k+k}{2}\right)=\left(1,\frac{3k}{2}\right)

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