Question 206984
Let's make the midpoint of the two points *[Tex \LARGE \left(x_{1},y_{1}\right)] and *[Tex \LARGE \left(x_{2},y_{2}\right)] be the point *[Tex \LARGE \left(x_{m},y_{m}\right)]. In other words, the midpoint is *[Tex \LARGE \left(x_{m},y_{m}\right)]



If we do that, then....


*[Tex \LARGE x_{m}=\frac{x_{1}+x_{2}}{2}] and *[Tex \LARGE y_{m}=\frac{y_{1}+y_{2}}{2}]



So in this case, we know that the midpoint is (3,-4) and we're given one endpoint of (-4,-6). So this means that *[Tex \LARGE \left(x_{1},y_{1}\right)=(-4,-6)] and *[Tex \LARGE \left(x_{m},y_{m}\right)=(3,-4)]



In other words, *[Tex \LARGE x_{1}=-4], *[Tex \LARGE y_{1}=-6], *[Tex \LARGE x_{m}=3], and *[Tex \LARGE y_{m}=-4]



So plug these values into the formulas 
*[Tex \LARGE x_{m}=\frac{x_{1}+x_{2}}{2}] and *[Tex \LARGE y_{m}=\frac{y_{1}+y_{2}}{2}] to find the point *[Tex \LARGE \left(x_{2},y_{2}\right)]



I'll let you do that. Let me know if you still need help.