Question #238218

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


1
Expert's answer
2021-09-19T18:07:04-0400

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=5𝑥+12𝑦+1152+122d=\frac{|5𝑥 + 12𝑦 + 11|}{\sqrt{5^2+12^2}}


Now, substituting the values,


d=5×(3)+12×2+1125+144\Rightarrow d = \frac{|5\times (-3)+12\times2+11|}{\sqrt{25+144}}


d=15+24+11169\Rightarrow d = \frac{|-15+24+11|}{\sqrt{169}}


d=2013\Rightarrow d = \frac{20}{13}


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