Bermuda Triangle has its vertices at points A(1,2), B(3,8) and C,(7,4). Polly island is located at (0,0). A person flies from (4,8) straight to Polly island. Does he pass over the Bermuda Triangle? If so, for what distance is he over the waters of the triangle?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The points that make up Bermuda Triangle are A(1,2), B(3,8) and C,(7,4). Polly island is located at (0,0). The person flies from (4,8) to Polly island.

The equation of the line joining B and C is (y-3)/(x-8)= -1

=> y - 3 = 8 - x

=> x + y - 11 = 0

The equation of the line joining (4,8) and (0,0) is y/x = 2

=> y = 2x

First find the point of intersection of the two lines.

x + y - 11 = 0

=> x + 2x = 11

=> x = 11/3

y = 22/3

The line also passes through A(1,2)

The distance between (11/3, 22/3) and (1,2) is sqrt((11/3 - 1)^2 + (22/3 - 2)^2)

=> sqrt(64/9 + 256/9)

=> (sqrt 320)/3

The person flies over the Bermuda triangle. The distance for which he is over the triangle is (sqrt 320)/3.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team