Question

The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find

(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)​

Answer 1

(a)

`3 √(5)`

(b)

`(6)/( √(5) )`

Explanation:

A(-3,0)

B(0,6)

`d = \sqrt{{( - 3 - 0)}^(2) + {(0 - 6)}^(2) } = √(9 + 36) = 3 √(5)`

`d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^(2) + {b}^(2) } }`

2x-y+6=0

a=2, b=-1, c=6

x0=0, y0=0

`d = (6)/( √(4 + 1) ) = (6)/( √(5) )`