If a(−1, 1), b(−4, 5), c(−9, 5), and d(−6, 1) are the vertices of a quadrilateral, do the points form a rhombus? justify your answer.
yes, it is a rhombus because the slope of diagonal segment bd equals negative two and the slope of diagonal segment ac equals start fraction one over two end fraction full stop
yes, it is a rhombus because the slope of diagonal segment bd equals two, the slope of diagonal segment ac equals negative start fraction one over two end fraction, and the diagonals bisect each other.
yes, it is a rhombus because the midpoint of diagonals segment bd and segment ac is (−5, 3).
no, it is not a rhombus because the slope of diagonal segment bd equals two and the slope of diagonal segment ac equals negative start fraction one over two end fraction full stop

Yes, it is a rhombus because the slope of diagonal segment BD equals 2, the slope of diagonal segment AC equals -1/2, and the diagonals bisect each other.

Step-by-step explanation:

The slope of diagonal BD is ...

  slope BD = (change in y)/(change in x) = (-4/-2) = 2

The slope of diagonal AC is ...

  slope AC = (change in y)/(change in x) = (4/-8) = -1/2

The midpoint of BD is ...

  ((-4, 5) +(-6, 1))/2 = (-10, 6)/2 = (-5, 3)

The midpoint of AC is ...

  ((-1, 1) +(-9, 5))/2 = (-10, 6)/2 = (-5, 3)

so the diagonals bisect each other.

While the third statement is true (both midpoints are the same), that fact alone is not sufficient to allow the figure to be declared a rhombus. The diagonals must also be perpendicular (have slopes whose product is -1). The appropriate answer choice is the second one:

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation: