Question

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

Answer 1

d)
`2√(26)` units

The perpendicular distance from the point to the line is

`d = 2 √(26)` units

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 = \fracax_(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{\sqrt{a^(2)+b^(2) } }`

`d = \frac{\sqrt{(5)^(2)+1^(2) } }`

`d =(-50-5+3)/(√(25+1) ) = (|-52|)/(√(26) )`

`d = \frac{2 X {26} }{√(26) }`

`d = (2 X √(26) X √(26) )/(√(26) )` ( ∵ 26 = √26 × √26)

`d = 2 √(26)`

Final answer:-

The perpendicular distance from the point to the line is

`d = 2 √(26)`