124k views
3 votes
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)​

User Swapab
by
8.1k points

1 Answer

6 votes

Answer:

(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) )

User Tushar Kolhe
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories