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

Exercises 118 Complete The Following 1 Find The Distance Between The Line And The Pointc X 2y 12 4 6 class=

Sagot :

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

[tex]d=\frac{|ax_0+by_0+c|}{\sqrt[]{a^2+b^2}}[/tex]

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

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

So the distance for letter c) is 4√5.

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