# 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...

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?

justaguide | College Teacher | (Level 2) Distinguished Educator

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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.