Answer:
k = 2
Step-by-step explanation:
We'll need the Midpoint Formula: the midpoint of a segment joining points [tex](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)[/tex]. 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
[tex]\left(\frac{-3+5}{2}, \frac{2k+k}{2} \right)=\left(1,\frac{2k+k}{2}\right)=\left(1,\frac{3k}{2}\right)[/tex]
That last expression is the centre of the circle; it is the same as (1, 3).
[tex]\left(1,\frac{3k}{2}\right)=\left(1,3\right)\\\frac{3k}{2}=3\\3k=6\\k=2[/tex]
