Answer to Question #238218 in Geometry for Uplinking Kelvin

Question

Q2. Find the distance of 𝑃(−3,2) from the line with equation 5𝑥 + 12𝑦 + 11 = 0.

Answer 1

The given point is 𝑃(−3,2)

Equation of line is 5𝑥 + 12𝑦 + 11 = 0.

We know that the distance between point and line is

$d=\frac{|5𝑥 + 12𝑦 + 11|}{\sqrt{5^2+12^2}}$

Now, substituting the values,

$\Rightarrow d = \frac{|5\times (-3)+12\times2+11|}{\sqrt{25+144}}$

$\Rightarrow d = \frac{|-15+24+11|}{\sqrt{169}}$

$\Rightarrow d = \frac{20}{13}$