Answer with explanation:
Coordinates of A and B are which forms a Line = A (-3,3) and B (1,4).
Line Y Z ,contains the points , Y (-4,7) and Z (-2,y).
let, y=k.
→Slope of Line joining two points is given by:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
→Slope of line AB is
[tex]m_{1}=\frac{4-3}{1+3}=\frac{1}{4}[/tex]
→Slope of Line Y Z is:
[tex]m_{2}=\frac{k-7}{-2+4}=\frac{k-7}{2}[/tex]
→Line AB and Line YZ are Perpendicular.
So,Product of their slopes = -1.
[tex]m_{1}\times m_{2}= -1\\\\\frac{1}{4} \times \frac{k-7}{2}= -1\\\\ k-7= -8\\\\k=-8+7\\\\k=-1[/tex]
→ Y coordinate of point Z = -1
Option A: y=-1
