Question

An aeroplane has crashed in the desert at a point that could be labelled (-15, 12) on a particular grid system. A search party sets out by a Four Wheel Drive from (18,3) and travels in a straight line passing through the point (3,9) and a light plane sets out from point (3,-15) and travels in a straight line passing over the point (-3,-6).

Will either of the search parties pass the point where the aeroplane lies if they continue on these paths? Explain how obtained your answer.

Answer 1

The search parties found will pass the point where the plane lies if the point lies on line connecting points through which the search parties passes.

Equation of line 1:

=> 5(y-3) = -2(x-18)

=> 5y- 15 = -2x + 36

=> 5y+2x = 51

On putting x= -15 and y= 12 , equation doesn't satisfies. So this search party will not pass through the aeeroplane.

For 2nd search party, eqn of line

=> -2(y+15) = 3(x-3)

=> -2y-30= 3x - 9

=> 3x+2y = -21

On putiing x= -15 and y= 12, equation satisfies. So m this search party pass through the aeroplane.