The midpoint is the average of the coordinates.
Let the coordinates of J be [tex](x,y)[/tex]
[tex]M = \frac 1 2(J+ K)[/tex]
[tex](-6,-2) = \frac 1 2( (x,y)+ (-2,4))[/tex]
That's really two equations:
[tex]-6 = \frac 1 2 (x + -2)[/tex]
[tex]-12 = x + -2[/tex]
[tex]x = -10[/tex]
[tex]-2 = \frac 1 2(y+4)[/tex]
[tex]-4 = y+4[/tex]
[tex]y=-8[/tex]
So we have J(-10,-8)
Check:
[tex]( (-10+-2)/2, (-8+4)/2)=(-6,-2) \quad\checkmark[/tex]
