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Two sides of a four sided figure have negative slopes which are the endpoints of the sides of this figure

(-4,-4) (-4,-1) (-1, -4) (-1,-1)


-2,-4 (-1 -1), (1,-1) , (2 -4)


1,1 (2,4) (5, 4)( 4,1)


(1,4), (2,1) (5,1) (4,4)

Verified Answer :

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Answer:    (d) (1,4), (2,1), (5,1), (4,4).


Step-by-step explanation:  For the set of values (d)  P(1,4), Q(2,1), R(5,1), S(4,4),  the slope of side PQ is given by

\(m_{1}=\dfrac{1-4}{2-1}=-3\),

slope of QR is

\(m_{2}=\dfrac{1-1}{5-2}=-0\),

the slope of the side RS is given by

\(m_{3}=\dfrac{4-1}{4-5}=-3.\),  

and the slope of side PS is

\(m_{4}=\dfrac{4-4}{4-1}=-0.\),

and so, the slopes of two of the sides i.e., PQ and RS are negative.

In the rest three cases also, we can likewise check the slopes of all the sides, but we will see that we are not getting result from there. For example if we consider the values in case (a) (-4,-4), (-4,-1), (-1,-4), (-1,-1), the slopes are

\(\dfrac{-1+4}{-4+4}=\dfrac{3}{0}, \dfrac{-4+1}{-1+4}=-1, \dfrac{-1+4}{-1+1}=\dfrac{3}{0}, and \dfrac{-1+4}{-1+4}=1\), no two of them are negative. Similarly, we can check for all other cases.

Thus, the correct option is (d) (1,4), (2,1), (5,1), (4,4).


View image ColinJacobus

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