Answer:
[tex]37=5x-2y,\,1=5x-2y[/tex]
Step-by-step explanation:
If [tex](x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)[/tex] are coordinates of a triangle then area of a triangle is equal to [tex]\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Let point P be [tex](x,y)[/tex]
Put [tex](x_1,y_1)=(5,3),\,(x_2,y_2)=(3,-2),\,(x_3,y_3)=(x,y)[/tex]
Area of a triangle = [tex]\frac{1}{2}|5(-2-y)+3(y-3)+x(3+2)|[/tex]
[tex]=\frac{1}{2}|-10-5y+3y-9+5x|\\\\=\frac{1}{2}|-19+5x-2y|[/tex]
Also,
Area of a triangle = 9 square units
[tex]9=\frac{1}{2}|-19+5x-2y|\\\\18=|-19+5x-2y|[/tex]
±18 = -19 + 5x - 2y
[tex]18=-19+5x-2y,\,-18=-19+5x-2y\\\\37=5x-2y,\,1=5x-2y[/tex]
