Question

A house is built on coordinates (2,9). There is a water pipeline that runs along the line y = 2 3 x – 1. What is the approximate shortest length of new pipeline needed to connect the house to the existing pipeline?

Answer 1

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 ($x_1,y_1$) and the line Ax + By + C  = 0 is given as:

$d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }$

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, $x_1=2,y_1=9$. Therefore:

$d=\frac{|\frac{2}{3}(2)+(-1)(9)+(-1) |}{\sqrt{\frac{2}{3}^2+(-1)^2 } } \\\\d=7.21$