1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on the same lifeboat. The light beam from Ship A travels along the line y = 2x. The light beam from Ship B travels along the line y = x + 5. What are the coordinates of the lifeboat?

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

          Position of ship A: ( - 1 , -2 )

          Position of ship B: ( -4 , 1 )

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

         Spotlight Ship A: y = 2x

         Spotlight Ship B: y = x + 5

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

         Spotlight A = Spotlight B

         y = 2x = x + 5

         2x = x + 5

         x = 5 , y = 10

The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships.

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step-by-step explanation: