Question

1,6,36,240,1960, x
find x. ​

Answer 1

Step-by-step explanation:

A part of the line intersected between the axes is bisected at the point (2, -5).

we have to find the length of the perpendicular drawn from origin to the line.

solution : let line intersects x - axis at (α, 0) and y - axis at (0, β).

(2, -5) is the midpoint of (α, 0) and (β, 0)

using midpoint section formula,

2 = (α + 0)/2 ⇒α = 4

-5 = (0 + β)/2 ⇒β = -10

Therefore the equation of line is x/α + y/β = 1

⇒x/4 + y/-10 = 1

⇒5x - 2y = 20

now let length of perpendicular drawn origin to line is h

area of triangle = 1/2 × base × height

⇒1/2 × 4 × 10 = 1/2 × √(4² + 10²) × h

⇒40/√116 = h

⇒h = 10/√29

Therefore the length of perpendicular drawn from origin to the line is 10/√29 unit