Answer:
7.21 units
Step-by-step explanation:
The shortest length needed to connect the house to the existing pipeline is the perpendicular distance between the location of the house (2,9) and the line y = 2/3x - 1.
The perpendicular distance (d) between a point ([tex]x_1,y_1[/tex]) and the line Ax + By + C = 0 is given as:
[tex]d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }[/tex]
The line is given by y = 2/3 x - 1; 2/3x - y - 1 = 0. The point = (2, 9)
hence A = 2/3, B = -1, C = -1, [tex]x_1=2,y_1=9\\[/tex]. Therefore:
[tex]d=\frac{|\frac{2}{3}(2)+(-1)(9)+(-1) |}{\sqrt{\frac{2}{3}^2+(-1)^2 } } \\\\d=7.21[/tex]
