Q2. Find the distance of 𝑃(−3,2) from the line with equation 5𝑥 + 12𝑦 + 11 = 0.
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+11∣52+122d=\frac{|5𝑥 + 12𝑦 + 11|}{\sqrt{5^2+12^2}}d=52+122∣5x+12y+11∣
Now, substituting the values,
⇒d=∣5×(−3)+12×2+11∣25+144\Rightarrow d = \frac{|5\times (-3)+12\times2+11|}{\sqrt{25+144}}⇒d=25+144∣5×(−3)+12×2+11∣
⇒d=∣−15+24+11∣169\Rightarrow d = \frac{|-15+24+11|}{\sqrt{169}}⇒d=169∣−15+24+11∣
⇒d=2013\Rightarrow d = \frac{20}{13}⇒d=1320
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