Mathematics: Find the distance from the point (-10,-5) to the line y = -5x - 3.

he isnt chad so frick himStep-by-step explanation:...

Find the distance from the point (-10,-5) to the line

jonathanmagana112002

30.01.2022

d) $2\sqrt{26}$ units

The perpendicular distance from the point to the line is

$d = 2 \sqrt{26}$ units

Step-by-step explanation:

Step(i):-

Given point is ( -10 , -5)

Given line is y = -5 x -3

5 x + y + 3 = 0

The perpendicular distance from the point to the line is

$d = \frac{|ax_{1} + by_{1} + c|}{\sqrt{a^{2}+b^{2} } }$

Given line is 5 x + y +3 =0

a = 5 , b = 1 , c = 3

Given point is (x₁ , y₁) = ( -10 , -5)

Step(ii):-

The perpendicular distance from the point to the line is

$d = \frac{|ax_{1} + by_{1} + c|}{\sqrt{a^{2}+b^{2} } }$

$d = \frac{|5(-10) + 1(-5) + 3|}{\sqrt{(5)^{2}+1^{2} } }$

$d =\frac{-50-5+3}{\sqrt{25+1} } = \frac{|-52|}{\sqrt{26} }$

$d = \frac{2 X {26} }{\sqrt{26} }$

$d = \frac{2 X \sqrt{26} X \sqrt{26} }{\sqrt{26} }$ ( ∵ 26 = √26 × √26)

$d = 2 \sqrt{26}$

Final -

The perpendicular distance from the point to the line is

$d = 2 \sqrt{26}$

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