Question

length of the perpendicular from the straight line x - 2y - 5 = 0 drawn from the point (-3,-5) is​

Answer 1

Answer:

length of straight line= (-3)-2×(-5)-5=0

-3+10-5= 2

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Answer 2

The correct answer is $\frac{2}{\sqrt{5 } }$.

Given: The equation = x - 2y - 5 = 0.

Point = (-3, -5).

To Find: Perpendicular distance of point from the line.

Solution:

Perpendicular distance(d) of (p, q) from ax+by+c=0.

d = $\frac{ap+bq+c}{\sqrt{p^{2} +q^{2} } }$

Put the value in the formula.

Point = (-3, -5) and equation = x - 2y - 5 = 0..

d = $\frac{1(-3)-2(-5)-5}{\sqrt{1^{2} +(-2)^{2} } }$

d = $\frac{-3+10-5}{\sqrt{1+4 } }$

d = $\frac{2}{\sqrt{5 } }$

Hence, the perpendicular distance from x - 2y - 5 = 0 of the point  (-3, -5) is  $\frac{2}{\sqrt{5 } }$.

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