two lines are perpendicular when the multiplication of their slopes is equal to -1.
the slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\text{ }\frac{y_2-y_1}{x_2-x_1}[/tex]
Then, the slope of the lines that passes through A(4,2) and B(-1,y) is:
[tex]m_1=\frac{y-2}{-1-4}=\frac{y-2}{-5}[/tex]
From the picture, t passes through (-1, 2) and (2,4), then its slope is:
[tex]m_2=\frac{4-2}{2-(-1)}=\frac{2}{3}[/tex]
Then
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \frac{y-2}{-5}\cdot\frac{2}{3}=-1 \\ \frac{(y-2)\cdot2}{-15}=-1 \\ (y-2)\cdot2=(-1)\cdot(-15) \\ y-2=\frac{15}{2} \\ y=\frac{15}{2}+2 \\ y=\frac{19}{2} \end{gathered}[/tex]
