Question

Exercises 11.8 Complete the following: 1. Find the distance between the line and the point.(c) x + 2y = 12; (4, -6)

Answer 1

In order to calculate the distance between a line ax + by + c = 0 and a point (x0, y0), we can use the following formula:

`d=\fracax_0+by_0+c{\sqrt[]{a^2+b^2}}`

So, calculating the distance between the line x + 2y = 12 (that is, x + 2y - 12 = 0) and the point (4, -6), we have:

`\begin{gathered} d=\frac1\cdot4+2\cdot(-6)-12{\sqrt[]{1^2+2^2}} \\ d=\frac4-12-12{\sqrt[]{5}} \\ d=\frac-20{\sqrt[]{5}}=\frac{20}{\sqrt[]{5}} \\ d=\frac{20\sqrt[]{5}}{5}=4\sqrt[]{5} \end{gathered}`

So the distance for letter c) is 4√5.