Answer
$y=4$
Work Step by Step
Use: $m=\displaystyle \frac{\text{change in y}}{\text{change in x}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}.$
The product of slopes of perpendicular lines is $-1,\quad$ $(m_{1}=-\displaystyle \frac{1}{m_{2}} ).$
The slope of the line passing through $(2,3)$ and $(-2,1)$ is
$m_{1}=\displaystyle \frac{1-3}{-2-2}=\frac{-2}{-4}=\frac{1}{2}$
The line passing through $(-1,y)$ and $(1,0)$ has the slope
$m_{2}=\displaystyle \frac{0-y}{1-(-1)}=\frac{-y}{2}$
Since the lines are perpendicular,
$m_{1}\cdot m_{2}=-1$
$\displaystyle \frac{1}{2}\cdot(\frac{-y}{2})=-1\qquad $... multiply with $-4$,
$y=4$
